Rats have several basic uses:
1. The can increase the value of the cards in your deck, albeit making them fairly useless to play. This is actually very strong with the right scaling TfB's. Bishop, Apprentice, Salvager, Remodel, Forge, etc. are great with rats if you have something that can use them.
2. They trash any type of card and give you an action. This means that cards that can only trash actions (like grave robber) or that can only trash non-treasures (like Hermit) can use rats as an intermediate to eat up copper & then pitch the rats for something better (e.g. villages or silver).
3. They can pile out. Rats with an empty deck (because everything else is already in play) auto-depletes. This means 2 piles gone with you up on VP with a strong goons engine can end by just having two rats in hand and then playing out the other 18. You can also auto-pile out the rats with a VP lead based wholly on dual victory-action cards (e.g. great hall/nobles) already in play or with something hiding the VP cards from hand (i.e. Island, Nv, Haven). Another option is to just win by curses + whatever you can buy from your action cash as you pile out.
For instance, develop/rats is pretty decent. Say you have develop/rats/market out. You can rats away your estates and some coppers, and then play a develop on a rats. You auto-draw the silver and leave a market on top for next hand. If you have a strong 3/5 (e.g. Fishing village/rabble) you can hammer away at the rat's and build a strong engine with no other trashing. Because the number of rats in your deck grows exponentially, you are virtually all ways assured of hitting rats/develop and gaining a nice set of 5/3 cards. I haven't tried it yet, but I think you might be able to rush rats/develop/duchy (buying copper to rats) or better rats/develop/duchy/duke. Develop/rats/Igg may also be fun & work.
Another shot is to give out the curses while your opponent gives out ruins, empty both of those, rats out, and then buy an estate or duchy off a mountebank, fishing villages, festivals, or whatever.