My 5 year old likes Mario Kart, Nintendogs, Viva Pinate and a cheap Fireman game we picked up from the bargain bucket in Morrisons. Tried Animal Crossing but there's a bit too much reading involved so that's been put away for a while.
Just had a look around for it and it's Sam Power Firefighter.
Had a flick through some of his others, Rhythm Paradise was really difficult. Looked fun, one of these games where you've got to tap the stylus at the right time, but it's fiendishly difficult. Ollie actually beat my wife and got to the second level, I managed a whole 4. Carnival Games was ok for ten minutes and then got discarded.
Does the DSI play the old Gameboy Advance games? I picked up Franklin the Turtle, Excitebike and Super Mario Bros 3 for pennies and he plays those regularly, with them being older (particularly Excitebike and Mario 3 as they're from the NES originally) they're a little bit simpler to play but still keep them entertained.