Mario's Early Years Preschool Fun.

The hardest part about that game is the controls if you don't have the SNES mouse. (yes I actually own this and have played it)

Hey I didn't say I don't like the game.  To the contrary I love the game.  I've beaten it 5 times.  Yeah, Pokemon is probably one of the easiest game series.  That's why you have the online metagame though to make it a real challenge.  

New Super Mario Brothers, Bioshock, and Blue Dragon are incredibly easy IMO, though I'm hoping that when I play Blue Dragon on Impossible soon it might actually pose a challange.

Skyblazer. I love the game and it wasn't that easy at first but once you know everything it's almost embarrassing beating it in one sitting (but still damn fun). Doesn't help that Sky is a powerhouse either.

I gotta agree with the Donkey Kong listing further above. Of course the point of the game is more to aim for high scores, but you can see everything it has to offer in five minutes.

Interestingly, people acknowledge that the old arcade games are more about high scores than playing from beginning to end, but when more modern games attempt that style of play (Yoshi's Story or Yoshi's Touch n' Go) it's usually poorly received.

If we were discussing games that are not intended to be high-scoring, find-the-secret type games, I'd say the Wind Waker.

Devil May Cry 2. Even on the most difficult setting, its still easy.

Easiest next gen game has to be Blue Dragon on 360. I loved the game and it was gorgeous, but when you can win a lengthy RPG without dying ONCE...that's really, really bad. Even with its easiness though, it was still great....
Easiest oldschool game--hmmm....Nintendo, Zelda and Sega Genesis, Golden Axe were both pretty easy.

Warcraft III : the frozen throne - all missions were far too easy for me ,but well the story was nice and after 6 years I still play it online ,so it still is one of my fav games of all time :)

most rpgs. but they're long usually.... so.... ummm.... brain age