Screw logic/puzzle games...........Booooooooorrrrrrrrriiiiiiinnnnnnnnggggggggggggg!
Try Salamander Portable, Parodius Portable, Twinbee Portable, Princess Crown, some people like Taiko no Tatsujin Portable 1 & 2 (although not really me, and if i did want to play them i'd play on my DS).
That should be good for starters.