I'm sure I'm not the first one to see this combo, but I searched and can't find it mentioned anywhere, so I thought I'd try my hand at writing an article about it. This is my first article (first post actually) so feel free to comment and offer suggestions.
I want to preface this by saying that this is probably a combo for advanced players. It requires a careful balance, a knowledge of exactly what's in your deck, as well precise timing to pull off correctly, without which your deck could easily flop.
The gist of the combo is this: grab as many hermits as you can, then grab as many Market Squares as you can while you turn most of your hermits into madmen. Then, in one explosive mega-turn, use the Madmen to draw your whole deck then use the Market Squares and remaining hermits and madmen to simultaneously gain a whole bunch of golds and draw them into your hand, then buy a bunch of victory cards and end the game. Sound far fetched? Let me explain.
STEP 1 - Grab the HermitsIdeally you should open Hermit-Hermit, then on your next turns, use the hermits to gain more hermits in addition to buying any hermits you can afford. If you can't afford to buy a Hermit then don't buy anything that turn and let the Hermit you played change into a Madman. (Note, if you draw any of your Madmen then resist the temptation to use them! You'll need them later.) If you use the Hermits' trashing ability, make sure you leave at least 1 estate/shelter/useless card in your deck to trash later.
Ideally you should aim to grab 9 of the hermits, but if you can't grab 9 then 7 will work (5 is less useful, but maybe not completely disastrous). There isn't much use in gaining an even number of Hermits, so if you can't get the 9th or 7th Hermit, don't bother with the 8th or 6th. Move on to step 2 instead.
Step 2 - Turn Hermits into Madmen while grabbing Market Squares. Start grabbing as many Market Squares as you can. You do not need to empty the market square pile completely- it's a good idea to leave a few behind to pick up with your hermits on your megaturn if you think your opponent will leave them there.
At the same time start turning more Hermits into Madmen. Your goal should be to have exactly 3 more Madmen then you have Hermits (ie: 6 Madmen and 3 Hermits, or 5 and 2).
Also, beware of letting your deck grow too big (ie: if your opponent is filling it with curses/ruins and you are Hermit/MSing them into golds). The ideal deck size is 29 cards or less. You'll see why in the next step.
Step 3 - Determining when to pull the triggerI made this its own step because sometimes even when your deck is ready you will want to wait a few turns before pulling the trigger.
There are many things to consider when deciding when to pull the trigger, but here are the most crucial ones:
•Your deck: it should be 29 cards or less, and is composed of your starting 7 coppers, 1-3 Estates/Shelters, exactly 3 more Madmen than you have Hermits, as many Market Squares as possible, and maybe a gold or two.
•Your hand: it should have at least 2 Madmen in it, and you haven't been hit by any hand-size reduction attacks this turn. Pulling the trigger with only 1 Madman in hand is risky- you might miss drawing a second one.
•The kingdom: There should probably be enough nearly-empty piles that you can end the game quickly, and you want to make sure you don't wait too long and give your opponent(s) enough time to snatch up too many provinces.
Beyond this I don't know what else to tell you about deciding when to pull the trigger. At the very least I suggest that you practice this combo a few times solo or against a computer before trying it against a live opponent.
Step 4 - KaBOOM!Pulling the Trigger should go something like this:
Play your first Madman, drawing 4 cards.
Play your second Madman, drawing 7 cards.
Play your third Madman, drawing 13 cards. Assuming you kept your deck 29 cards or smaller, you should now have your whole deck in your hand.
Play your first Hermit, and trash that useless non-treasure card you have been holding on to this whole time. If you need more junk cards for your other hermit(s) to trash, make sure to pick one up now. Or if you can pick up those market squares you left behind to use later in the turn.
As a reaction to your trashed card, discard all of those Market Squares in your hand and gain a fistful of gold.
Play your fourth Madman, drawing all those golds and Market Squares.
Repeat with each Hermit/Madman pair that you have, using the last Hermit to pick up a silver, or maybe a card from a pile you want to empty.
Now you should have a giant hand full of Gold and Market Squares, with a spattering of copper. Play all of your Market Squares to get all the +buys that you need.
Now just buy up a bunch of Provinces and any cards you need to 3-pile the game (if needed).
StrengthsThis combo/engine has a lot going for it.
•It's very fast. It may not seem like it, seeing as it takes around 10+ turns to build it up, but unlike most other engines, the "mid game" and "end game" phases happen entirely on one turn. This also makes it rather surprising for your opponent if they haven't seen it before.
•It isn't really affected by most attacks, with one or two exceptions (see below). Since you really only need to be able to play one Hermit each turn, hand size reduction attacks are pretty much moot. They will still slow you down a little, but likely not enough to matter. Cursers or Junkers don't do much either, since (unless they are giving you coppers) you can use your Hermits to trash them out of your hand or discard pile.
•You only need to buy two cards (Hermit and Market Square) to pull this combo off, and both of them only cost $3. No need to build up to get the $5s or $6s or $7s.
• Both of the cards you need are from the same expansion, meaning that this combo should show up fairly often when you're playing with Dark Ages.
• Also, thematically, you have to admit this is one of the coolest/wackiest combos to play. You have droves of hermits wandering around outside of town, gradually going mad. Meanwhile you spend all your efforts building the largest grandest market square in the world, and then, on opening day, all of those insane hermits rush into town and run amok... And somehow you end up filthy rich and reigning over a massive kingdom.
Weaknesses• While this combo resists most attacks, Trashers (such as Knights or Saboteur) can destroy it, as you need a lot of the right cards to pull it off. Also, being hit by a hand-size reducer attack on the turn when you're ready to pull the trigger will stop it dead. If your opponent has built up an engine where he is Militia-ing you every turn it can be devastating.
• While you only need two types of cards, you need a LOT of those two cards. If your opponents are snatching them up as fast as you are it will sap a lot of the strength out of your deck (However, in my experience, Hermit and Market Square don't tend to be very popular, so unless another opponent is going after the same combo you're probably fine).
• It is a high-skill combo, demanding a lot of attention to detail, and also requires a lot of buying restraint. It can be really hard to fight the temptation to buy that really awesome $5 card when you get a lucky hand of coppers, but don't do it!
Works well with: • Scheme: which will let you turn your hermits into madmen without having to trash them, and can be used to line up your Market Squares with Hermits. Also, at $3 it's perfectly priced for this combo.
• Haven: Great for lining up Market Squares with Hermits, and for lining up Madmen for your megaturn. Also, can possibly be used to increase your hand size so that you don't need as many Madmen when you pull the trigger. And again, $2 is a great price for this combo.
• Versus Cursers/Looters: all they do is give you fuel for your hermits and market squares to turn into gold.
• Other Cheap Trashers: can be substituted for Hermits during your megaturn if you weren't able to get as many as you wanted.
• Talisman: as an opener it can help you pick up components faster.
Sample Games: (Unfortunately I haven't played on any of the computerized versions of Dominion, so I don't have any records of games I have played to show you. Several people have posted their games in the comments though.)
In solo play I was able to set it up and was ready to pull the trigger by turn 12, but didn't have any Madmen in my hand so I had to wait until turn 13. With 9 Hermits/Madmen and 9 Market Squares I ended up with over $70 to spend and 10 buys. Of course that would be the perfect situation, and not very likely in a real game.
I finally got a chance to try this against real opponents: it was a 3 player game, and I was able to snatch 9 Hermits and 5 Market Squares, and then I pulled the trigger around turn 12 (I lost track exactly) which was actually too early- I miscounted, and only had 5 madmen to my 4 Hermits (instead of 6-3) and the Kingdom wasn't to the point where I could immediately end the game, but it still worked beautifully. I ended up with $35 and 6 buys, netting me 4 provinces and several Estates from my Hermits. Over the next several turns I was able to use all that gold to grab 2 more provinces and empty the estate pile to end the game well in the lead.)
Edit: Thanks again everyone for all your input! And Thanks to the Dominion Strategy Gods for deciding to feature this article on the main page. It makes me feel special. 
Added Haven to the "Works well with" section, and fixed Scheme. It turns out Scheme does NOT work for lining up Madmen. 
I would still love to see some sample games that show mirror matches and/or attempts to block this combo while using another strategy. If you have any, please share!
