I would suggest a few "trendy" games in each case, just in case you wanna give it a go:
Lost Cities
Author: Reiner Knizia
For 2 players only
Lost Cities | Board Game | BoardGameGeek
Keltis
same author, almost same game, for multiple players
Try to get some help at the above site as well, they've got an enormous database for this.
cybermike: I was going to suggest something like Magic or the World of Warcraft cardgame. They're actually fun (I tend to like WoW cardgame better), but I'm not sure if it's the kind of game he's looking for, especially since the idea is to buy alot of cards and trade them. (the standard starter-decks are not quite as fun)