i think the only time i got a huge first party game was SMB2, which I had played a lot at a friend's house before christmas. On hanukkah, my parents would just hand me the gifts. (we celebrated both, but I'd usually get, like socks or notebook paper for hanukkah.) That happened a lot-- some friend would get the big release on release day and I'd get to play them enough to not want to waste a Christmas slot on them. Zelda 2, Castlevania 2, Double Dragon 1+2, etc.
I'd usually ask for weird third party games without having played them first, because they'd look cool in Nintendo Power. Or I'd ask for them, then rent them when they popped up at Blockbuster, and pass judgment beforehand-- Battletoads was one of those. I tried rescinding my wish list at the last minute on that one but it didn't work. Bad Dudes was kind of a let down, after seeing screenshots of guys beating up ninjas. Super Dodge Ball was awesome--had already played it, but wanted to own a copy. Final Fantasy 1 was prob the most excited I was for a NES game, but I think I got that for a birthday. I got Xenophobe one year...ugh. I figured out in 10 minutes that game was ass.