I find Ill-Gotten Gains in Dominion Hinterland to be such a clogger, with all the curses and coppers it generates. How can I beat a player who keep getting the Ill-Gotten Gains when there are no trashing cards available?
Not sure which Dominion expansions are you running, but there are several cards that can counter this.
If you have prosperity, you can add the Watchtower to the kingdom cards which blocks curses gained in this manner, priced at only 3$. With Masquerade from Intrigue, or Ambassador from Seaside you can give those curses back to your opponent. Dark Ages has several cards which work with trashing.
On the other hand, if you put a more valuable 5$ card you can rush that instead of going for IGG. Embargo from Seaside also works wonders.
As the other poster states, if there is no counter focus on going for duchies as well as any other victory cards placed in the kingdom set.
The major thing to understand about heavy ill-gotten gains strategies is that they rapidly deplete two piles: both ill-gotten gains itself and the curse pile.
This means that ill-gotten gains games tend to end based on a third pile running out rather than the province pile depleting, and so you need to adjust your strategy to compensate -- notably it makes duchies a lot more attractive, and all the extra junk in your deck makes the free copper you get from running ill-gotten gains' effect more attractive.
So, while this obviously varies from game to game, barring some more effective game specific strategy my usual answer is to take ill-gotten gains and duchies.