A loaded question. With over 650 licensed titles there are a TON of awesome games. For RPGs, go with Final Fantasy, and the Dragon Warrior series. Crystalis is also good. If you like shmups, get Life Force and Gradius. For action-platformers, go with Castlevania and Ninja Gaiden. For straight platformers, the Mario series is always a good choice. Puzzle games, try Tetris, Wario's Woods, and Hatris. Lolo series is also good for puzzles. Contra and Super C are must-haves as well. If you like beat-em-ups, get the Double Dragon games (#2 is the best IMO). And then of course there's always Zelda, which every NES owner should have on-hand.
That should give you a good starting library which won't cost you an arm and a leg and hits on the most popular titles. I could really spend a half hour going through all the worthwhile titles on the system, some rare (and expensive), others just not as well-known, but the above should give you a good start. Have fun, and enjoy your NES!