Everybody loves Mario Kart!
I'm not sure really, everyone develops differently. At five and six I was playing things like Sonic, Mario 64, Wave Race, Pilotwings, etc. which are all certainly more complicated than Dora. Mario Kart Double Dash might be a good choice depending on their skill level.
Super Mario Sunshine and Zelda: Wind Waker are kid-friendly, but controlling the character and the camera at the same time might be too complicated. Wind Waker is also probably way too difficult for them, so I'd go with Mario before that.
Then maybe look at some Mario Sports titles (other than golf...). Super Mario Strikers may be a bit too fast-paced, but it's loads of fun and very simple. Mario Superstar baseball is very simple but could be a little frustrating for some, and most of all it's pretty boring too

Mario Tennis, perhaps?
The Mario Party series is also great fun, they're made up of a bunch of mini-games strung together by a board game interface. It's a great multiplayer game, too, and the games are usually very simple. I'd definitley look into Mario Party.
Donkey Konga is a great game that uses the bongo peripheral for the Cube to play to music (it's packaged witht he game, and extra ones can be bought separatley). However, if your kids haven't really developed good hand-eye coordination and timing yet it'd be very dificault and frustrating. I'd guess your 7-year old would be able to handle the easy stuff.
There's also Kirby Air Ride, which may be the best choice. It's a very simple and bright racing game that only uses the A button. It takes a while to get used to and may be a little too hectic, but it's extremely simple and very fun.
Look into those, those are the only ones that I know of that are simple and fun, but really they might all be a little too much for your kids. I know at that age my little brother wasn't able to play half those games.
My biggest reccomandation by far, however, would go towards the purchase of a Game Boy Advance or a Nintendo DS portable system. The GBA library has TONS of liscensed children's games starring numerous cartoon and television characters that I'm sure your kid would love. The Nintendo DS is a bit more expensive, but it's the console that publisher and developers will be supporting in the future. Plus it's way cool, what with the touch-screen and such, I'm sure your kids will love it. The DS is also backwards compatible with the GBA, meaning your kids can play all those great Game Boy games on their DS too.