Of my favorite side-scrollers, Abe's Oddysee, Out of this World, and Vice: Project Doom, keep swapping back and forth.
Abe's Oddsysee has an advantage over both of those games: I like the character.
We have all been situations where we are self-serving. Abe is simply trying to save himself from being eaten. In the process of doing so, however, Abe inadvertently becomes the chosen one of the Mudokons, and must embark on an adventure to save his kind. Despite Abe being an alien, I found his character extremely relatable and likable.
The gameplay is somewhat different than most side scrollers. Every one of your actions; every step, every jump, and every move must be deliberate and thought out. If you simply try and run to the end of a level, you most likely will be killed. The controls are a bit stiff, but nothing crippling, and I could always make Abe do what I needed him to do.
The atmosphere and environments are very well defined, and the game has a sense of humor. While the game is a little violent, I think most kids could play it without any emotional damage.
The game is very difficult, but you have unlimited lives, and you can save at any point.
I highly recommend this game to anyone who likes a good side-scroller.