My articles have gotten mixed reviews so far, but I figure I'll keep trying. I feel I know more about this than Death Cart, anyway.
(in progress)
Shelters are the most drastic change made to Dominion by the Dark Ages expansion. They were saved for last in the previews before release, after we saw the trash-gainer, the $1 cost card, the Ruins and their Looters, the upgrading cards, and Spoils. While each of those do change the game in their own ways, ranging from the subtle to the not-so-subtle, they certainly more or less fit into the game space of Dominion as we know it - at the end of the day, they are simply Kingdom cards with cool, new effects. But Shelters change how we play Dominion at a fundamental level.
As we've known since our first game, our deck in Dominion starts off with seven Coppers and three Estates - we're so used to this concept that we plan our entire strategies around knowing this. We think about the risk of opening with two terminals, we consider whether trashing Estates is worth losing the points they give, we see the power of Ambassador and Baron as opening buys, and we rest easy knowing our first Silk Road will be worth at least 1 point. Shelters throw all those concepts out the window, and give us some new ones.
First, they all cost $1, which means that you can no longer Remodel a starting card into a Smithy or Militia, and Bishop has been gypped 3 victory points, among other things. Next, they all do something - you are now starting the game with cards that have text on them - get out those reading glasses. Third, you no longer start off with 3 Victory points, so strategies that trash into engines no longer have to worry about a tie-breaking Estate. Finally, only one of them is a Victory card, which has ramifications to be discussed in time.
Let's look at each Shelter one by one.
Necropolis is easily the most useful of the Shelters, and, at first glance, would seem to be the only reason why anyone would ever want to use Shelters. Having a card give +2 Actions from the beginning of the game is immensely helpful. I often catch myself disparaging at the lack of Village on a board with good terminals, before remembering several turns in that I have Necropolis. It's not all that much of a help, but every little bit counts. Necropolis is very useful on engine boards, as you already have a Village in your deck from the beginning, allowing you to start your engine sooner.
Hovel, at first glance, seems to be the least useful. It is probably the closest we will ever come to a Dominion card that is just a Reaction and nothing else. Being able to trash a card upon buying a Victory card is not completely new - Farmland introduced us to this concept in Hinterlands. But Hovel allows you to do this when buying any Victory card, so long as the card you're trashing is Hovel. So what is the point of this? It allows that Province buy to be just a little bit less harmful to your carefully crafted engine, as instead of adding to your deck, it is replacing a card. Perhaps the only time you'll want to save Hovel from trashing is in a Gardens game, where every extra card counts. Now, some of you may be tempted to buy an Estate during a 5/2 open on a board with no good $2s. This would be a mistake. Hovel's power comes in using it on a Victory card you would have bought anyway. If you trash Hovel to an opening Estate, your deck is not hurt, and you're 1 point ahead, but now that Province buy is once again adding to your deck instead of replacing a card, and that extra junk card may cost you the win. The player who saves his Hovel has just as much junk as you do until that Province buy - then he has less. Now, if you can think you can make a really quick three-pile ending before your opponent has a chance to pick up any Provinces, then Hoveling an Estate might be a good idea, as winning 1-0 is still winning. But, how often will such situations arise? More realistically, the edge case where you'd want to trash Hovel to an Estate on a 5/2 opening would be with Bishop on the board; since you'll be trashing the Hovel/Estate anyway, might as well replace the Hovel with Estate, since you'll get more points out of trashing it to Bishop. Hovel is also good for Kingdom Victory card strategies (excepting Gardens) since you want those cards earlier than you do Provinces, so you can win the split. Being able to trash away an otherwise useless starting card is very helpful. Of course, if you have the opportunity to trash away Hovel before this, such as to a trasher of your own, or someone else's Bishop, you might as well.
Overgrown Estate has a cute little on-trash bonus, but not much else going for it. It means that Scout is not completely useless in Shelters games, but it really doesn't do anything else. A cute trick is Hermiting an Overgrown Estate from your discard to let you draw a card. But +1 card one time is cute, and not much else more. Perhaps the best use of Overgrown Estate is when your opponent plays a Bishop, so you can swap it out for a hopefully better card in your hand.
Now let's discuss the drawbacks of no longer having Estates in your deck. Ambassador has no idea what to do with Shelters, since they're not from the Supply, turning him into a Copper giving card. Baron is completely neutered, unless you have a desire to gain free Estates. Hunting Party trips over them, Silk Road is now initially worth .5 points (rounded down), and Rebuild has a lot more extra work to do - funny, for a Kingdom card that comes packaged in the same set as Shelters. Oh, and Remake and Upgrade can't give you Silvers anymore.
Now, what are the benefits? Menagerie is now conceivable as an opener, and becomes much easier to trigger. Fairgrounds becomes much easier to bring to 6 VP without buying Curses, and Harvest yields $4 much more consistently. Fortune Teller reacts interestingly - it now effectively discards your opponent's entire deck in the beginning - this can prove very annoying if it prevents them from playing or lining up key cards - one IRL game I played had me frustrated for a few turns as a Fortune Teller prevented me from lining up my Urchin with my Marauder to get a Mercenary. Death Cart has an extra Action to trash from the get-go. And, as mentioned earlier, since everyone starts with 0 VP, you no longer have to worry if trashing your opening Estates will cost you the win.
So, in general, cards that interact with Victory cards are weakened in Shelters games, but most cards that deal with trashing, engines or hand/deck variety are bolstered.
Bear in mind, though, that Shelters are, according to the rules, only supposed to show up in majority Dark Ages games, just like Colony and Platinum are only supposed to show up in majority Prosperity games. So Shelters, while game-changing, has not upset the entire Dominion paradigm, and you can choose not to play with them if you wish. But personally, I feel that, other than making Baron a sad panda, Shelters make for a more interesting, enjoyable Dominion experience.