My entire library, because trade-ins never get you a good value on games. I traded in some games once, and even though they were mostly either duplicates of games I already had or ancient sports games that I didn't want, but came in a bundle with some games that I did want, it still left a bad taste in my mouth.
As for games that I would never trade, no matter how much money somone offered me? That would be my copy of Final Fantasy VII, my (semi-rare) gray Player's Choice edition of The Legend of Zelda, my copy of Super Mario Bros/Duckhunt/Worldclass Trackmeet, and probably a couple of other things I'm forgetting, because they all hold sentimental value to me. There's some things you just hang onto.