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[Powerman]

Introduction
Each Dominion game has 10 kingdom cards, and each card plays a role in determining the optimal strategy on each board.  Part of the beauty in Dominion is that no card dominates every single board, and no card is completely useless in every single board.  Rather, like in an ecosystem, each card fills a specific niche.  And like in an ecosystem, when one of these niches is not filled, the ecosystem (or board) does not operate as can be expected.  But when everything clicks, great things can happen.  The question is, what are these niches to be filled?

The Niches of the Dominion Ecosystem (in no particular order)
Attacks
Attacks are like the predators of the Dominion kingdom.  They keep the rest of the board in check, and you ignore them at your own peril.  Even weak attacks can change how a game is played, so an important first thing to look at in every kingdom is if there is an attack.
+ Buy / + Gain
Gainers / Additional Buys are like the weeds of the Dominion kingdom.  They allow for seemingly uncontrolled deck growth, but without a plan they quickly become pests.  The ability to gain multiple cards in a turn not only allows for Gardens to have the potential for viability, but also allow for building engines quicker (2 cards per turn grows faster than 1) and can screw up end game timings / PPR.
Alternative Victory Cards
Alternative Victory cards are like the tall trees of the Dominion kingdom.  They can slightly protect you from the burns of an unfavorable province split, but often cannot keep you safe forever.  In a game with no extra VP cards / chips, a player needs 43 VP to guarantee a win.  But adding in even the lowly Great Hall, and that total goes up to 47.  With Alt VP cards that can provide more points (SR, Gardens, etc.), it becomes even tougher to get to half the points, and opens the door for the player that doesn't win the province battle.
+ Action
Additional actions are like the water supply of the Dominion kingdom.  There is only so far you can go in games without a way of getting +Actions, and if you forget about +Actions you will lose the game.  +Actions normally mean villages, but it can also be in the form of KC, TR, Golem, etc.  In a game without any +Actions on the board, you are only able to play one action card a turn regardless, so this limits the options of what you can do with the board. 
+ Card
If additional actions are the water supply, then more cards are the food source.  No great deck is complete without the proper card drawers, but if you have too many, you'll get sick.  Without these cards, you will never be able to have more than 5 cards in your hand, which means mega-turns become near impossible.  It's great to have lots of actions to play your bridges, but if you only get 3 in hand you hardly can dominate.  + Cards come in the obvious form (Smithy, Laboratory, etc.), but your hand size can increase in more subtle ways (Adventurer, Native Village, KC-ing a cantrip, etc.).  Without a way of +Cards, combos become increasingly difficult to form.
Sifters
While + Cards might be the main food source, sifters act as a healthy alternative.  Your handsize is not increasing, but it can sure feel like it is, as you can get rid of your bad cards and get good cards to replace them.  The main ones here are Warehouse and Cellar, but any Draw / Discard card works here.  These enable good turns, and can often end up being as strong as just a + Card, especially if you have mostly good and bad cards, and few middling cards.
Virtual +$
Virtual dollars are like the... well, they don't really compare to anything.  Basically, the presence or lack thereof of these tells you whether you are going to need many or few silvers / golds.  This can be as simple as a Woodcutter, or a card such as Vault.
Opponent Interaction
Opponent interaction are like the insects that pollinate flowers.  They generally make growth faster, but at least for awhile, you don't notice if they're gone.  These cards can be positive (ie. Council Room), negative (ie. Any Attack), or "neutral" (ie. Tribute).  It is important to take note of these because they force you to "stop playing solitaire".  If your opponent buys a Masquerade, you're probably going to want to have some weaker cards to pass.  If he gets a Bishop, that might mean you don't need your own trashing.  If he's using Council Room a lot, you might need less +Draw in your deck, etc.
Trashing
Lastly, trashing is like the bulldozer that comes in and destroys the existing habitat.  By getting rid of the natural habitat (estates + coppers), there is room for bigger and better things to be built.  These fall into two categories: trashers (ie. Chapel) and trash-for-benefit (ie. Apprentice).  While both of these are valuable early (albeit the pure trashers are much quicker), trash-for-benefit remain useful late.  Knowing which of your weak cards you can get rid of and which you can't can shed great light into what type of a deck you should build.

So what does all this mean?
Most of what has been said so far is pretty basic / straightforward knowledge.  What I am trying to shed light on, is how to apply this knowledge to make a great deck and win games.  Most people know that a deck without their estates and coppers in the end is going to be better than a deck with them, but most also know that trashing can be to slow to catch up to simpler strategies that keep their junk.  The easy answer might be "if you can make an engine", but I have seen many times where an engine loses to a strong BM, say BM-Courtyard.  This is not about making engines, it's about noticing interactions between cards, and identifying which cards will be strongest on a board, and how to best utilize them.

The best way to show this is by analyzing real game boards, where it looks like multiple strategies could be strong.  First I want to point to a post by Theory where he touches on this issue with his two example boards, and how the niche of +Actions changes how the game is played.  Now onto real games:

Game 1 (Link):
Board: Apothecary, City, Festival, Hoard, Horn of Plenty, Oracle, Potion, Scheme, Spy, Vineyard, and Warehouse
First of all, let's see which of the niches are filled by which cards:
Attacks: Spy
+ Buy / + Gain: Festival, Hoard, Horn of Plenty (Eventually city)
Alternative Victory Cards: Vineyards
+ Action: City, Festival
+ Card: Apothecary, Oracle (Eventually city)
Sifters: Warehouse
Virtual +$: Festival
Opponent Interaction: Spy
Trashing: None
So most of the roles are filled... except trashing.  This can make it difficult to build an engine, and with the only attack being spy, the game is likely to be pretty fast.  There are plenty of ways to gain multiple cards, and plenty of Village support to play these cards.  The +Draw is weak, as it is limited to Coppers or a +2, but there is pseudo + Cards from warehouse.  There is an Alt. VP in Vineyards, but that requires potion so it might be just too slow without any attacks.  Now to the actual game.  The first 6 turns we buy the same cards, so it appears as if we might be mirroring, but in turn 7 and 8 we both announce our true intentions.  He gets a Province and a Hoard, so it is clear he wants to go for provinces and use the hoard to generate golds.  I keep buying / gaining actions, even when I start hitting $8.  What could I be doing?  It might or might not seem obvious now, but I was going for Vineyards!  This caught my opponent off guard, as he was stuck between Provinces and Vineyards and by the time he realized what was going on, there was absolutely nothing he could do.  So what were the key cards here?  Well it'd be easy to say just Vineyards, but without a lot of actions, you won't be able to beat provinces.  I'd say the key cards were also Apothecary as that gave me the much needed draw, and Horn of Plenty as I was able to gain action cards from it every single turn.  They were key cards because of the Vineyards, so even though they may not be the technically strongest cards, they acted as the strongest cards.

Game 2 (Link):
Board: Apothecary, Apprentice, Baron, Bridge, Contraband, Crossroads, Merchant Ship, Potion, Stables, Trade Route, and Wishing Well
Again, let's see which of the niches are filled by which cards:
Attacks: None
+ Buy / + Gain: Baron, Bridge, Contraband, Trade Route
Alternative Victory Cards: None
+ Action: Crossroads
+ Card: Apothecary, Apprentice, Crossroads (potentially), Stables, Wishing Well (potentially)
Sifters: None
Virtual +$: Baron, Bridge, Merchant Ship
Opponent Interaction: Trade Route
Trashing: Apprentice, Trade Route
The first thing to notice about this board is there are no attacks at all, so your gameplay can be very independent of your opponents.  Second, there are no Alt. VP cards, so the person with the most provinces is probably going to win.  Third, the only +Action is Crossroads, which means on a given turn you can play up to 3 terminal actions.  Finally, there are lots of different options for getting big hands, and they have some interaction with each other.  My opponent and I take our different routes from the beginning, with him going for Baron, in hopes of using its early $ Boom to get gold and then quick provinces, which works as he wanted it to.  I go for Apothecary, as it gives +Card, plus makes Wishing Well better, plus gives coppers to discard to stables.  We both play out our decks until turn 14, where I draw my deck and have $11, 4 buys, things cost $3 less, and there are 3 provinces less.  For VP, I can either buy 2 provinces, a province and 2 duchies, or 4 duchies.  I know that I am likely to keep drawing my deck, so I will have this option again.  I look to my opponent's deck.  He has $17, 3 buys, and $1 cost reduction possible, but then I look at his draw situation.  He has to use his stables for draw which means a lot of those $ will be in his discard.  Unless he uses his Crossroads to draw them.  But if he does, then he will not be able to play his Baron and Bridge.  So it is basically impossible for him to get to $16 to double province, so I choose the the province and 2 duchies.  As predicted, he gets very close, but cannot double province, I draw my whole deck and buy the last 2 provinces for the win.  So what were the key cards here?  Crossroads, as it gave the +Actions that were vital to both of us and gave us cards in the end.  And also Apothecary, as it gave me early economy, and drew, and enabled WW.  Note, the bridges are NOT key here, as they could have been equally replaced by Baron, as I was drawing my whole deck with my 3 estates, and 3 barons are ~ to 3 bridges.

Game 3 (Link):
Board: Expand, Explorer, Highway, Inn, Loan, Merchant Ship, Minion, Potion, Scout, Tunnel, and University
Again, let's see which of the niches are filled by which cards:
Attacks: Minion
+ Buy / + Gain: Explorer, Tunnel, University (kind of Expand)
Alternative Victory Cards: Tunnel
+ Action: Inn, University
+ Card: Scout (kind of Minion)
Sifters: Inn
Virtual +$: Merchant Ship, Highway
Opponent Interaction: Minion
Trashing: Loan
So what do I see in this board.  First off, there is a very strong attack in Minion.  But for minion to be strong you need A) a lot of minions, and B) few treasures / victory cards.  So this leads to trashing, which is limited to loan.  Loan actually is a decent trasher for Minion, as it will slowly get rid of your treasures without crippling your early economy.  But how to mass Minions.  There is no +Buy, so the two options are either expanding estates (which is strong) or by gaining them with University.  Expand, however is going to be tough to hit early, as getting to $7 without buying many treasures is not a simple task.  So I elect to go for University, opening Potion / Loan, while my opponent goes for Expand by opening Silver / Loan.  We get similar turn 3/4 luck, and on T5 we both get what we want: Expand for him, University for me.  Turn 6 is the turning point of the game IMO.  I get an unlucky 4, and I know I don't want more treasure... so I buy a Scout, in hopes of later on using it to clear junk off my deck to assure the Minion discard gets me a good hand.  He hits $5... and buys a Merchant Ship.  I'm not sure what he was doing, but from here I go on to pile drive minions, start gaining Highways once those are out and sail to an easy win.  Here, the key cards were Minion, as it acted as a pseudo +Card, and attacked him, and University as it allowed me to gain them quickly.  Highway added very little value to my deck, and would have been much better off as say, a Market, as without +Buy it isn't very good (although it did allow me to gain expand).

Conclusion
The point I'm trying to get across, is that in Dominion there truly is no "must buy always" card.  On some boards, even cursers are completely ignorable.  Before you start a game, you have to look and see how cards interact amongst each other.  This does not necessarily mean 2 or 3 card combos, but more of "what does this card need to be useful?  does this board have it?".  If you see bridge, is there draw and actions?  If you see King's Court, is there anything worth King's Courting?  Even the strongest of cards can be weak on a given board, and if you just assume a card will be good it might not be.  Dominion cards are not inherently strong or weak... other cards make them so.

Sorry for the bad biology analogies and thank you for reading.  I hoped this caused you to think a little, and maybe you thought of something you hadn't thought of before. 

[^_^_^_^]

I think the title is misleading. I came in here thinking "wait... you can choose which cards you attack? Either this is predicting the cards in your opponent's hand at any given moment or it is some misleading title... most likely misleading." I was right

A better title might be "Buying the Key Cards" or Finding the Key Cards"

[Titandrake]

Seconding that comment, I thought it would be about the importance of rushing, which is an article I've always sorta wanted to write but was far too short to be one, and I didn't feel experienced enough. But yeah, going into a game with a plan is always important. And not like "Oh I'll do Smithy-BM, whatever". More like..."Smithy is in the kingdom, but first I'll check if there's +Action/+Buy/attacks that slow me down/etc, and if nothing dissaudes me then I'll do BM." Accounting for potential problems, or deciding that BM is fast enough to win, rather than just playing BM and hoping it'll work. I'm phrasing this kinda badly.

(Small tangent: By "rushing", I mean the importance of winning certain splits. In a Minion/Hunting Party game, the person who wins the Minion/Hunting Party split often wins the game. Even if in the short run they have forgoed other key cards, in the long run the momentum of 6 Hunting Parties vs 4 will just crush the player with 4. The more subtle case is the engine case when there's only one source of +Actions on the board. Winning the Village split 6/4 or 7/3 will win you the game, as long as the game lasts long enough for you to capitalize on it. So on a big turn, it's okay to buy 3 Villages instead of Margrave + Village. Long run, you will draw way more cards and have way more buying power,since your opponent just won't be able to play as many terminals as you can. Anyway, this tangent was actually longer than my actual post, so my bad.)

[^_^_^_^]

plus, a lot of that was phrased badly and had bad examples. Experienced players can tell what you meant but new players will most likely have a problem. I can tell but thats because I've learned a ton already

[Powerman]

I changed the Title, hopefully that is more in line with the article.