When graphics power was scarce, side-scrolling was the norm in video gaming. Though the two-dimensional sprites littering the landscape of one street of LA painted from the side could potentially bog down the 3.58 MHz processor in the SNES, at least the system wasn't trying to render millions of interlocking triangles off in the isometric distance.
Why is side-scrolling awesome?
There are many sides to take in the "side-scrolling is awesome" debate.
Simplicity = Technicality
Drawing everything from the side isn't always about reducing polygon counts. Sometimes it reduces the freedom of motion to allow level design to be less lenient. 3D platformers have always been plagued with collision issues, pathfinding glitches, and broken geometry that side-scrollers never have to deal with. Rendering the world in 3D causes all these problems during programming and though they can be fixed, even the camera perspectives can make 3D platforming far more difficult than it feels like it should be. To compensate for this, many designers make their platformers either very forgiving on mistakes or make them easier.
Side-scrollers are not limited in this way. Because the perspective is always the same and the game's textures are all drawn to facilitate the angle you play at, figuring out what exactly is going on is always easier in a platformer. This increased understanding of the environment through simplicity allows these games to be made much harder than their free-roaming companions, with more tricks and more difficult timings.
Right is the right way in pretty much every side-scroller. This makes logical sense because most societies assume right to be the direction of progress or correctness, a fact linked to most people being right-handed. It is the flow of things. The direction Mario goes on his adventures is indicative of this natural human tendency. The only reason to go left, the direction of dubious or clumsy behavior, is to prepare for a large bound for a platform to right, absolving your decision to stray left in exchange for greater progress. You run away from your foes and scheme to the left; you succeed to the right. This seems a little silly, but its psychological and social ramifications are very real.
3D stuff is hard to edit and create. That's why it takes huge buildings full of programmers to make modern games. Editors pass most of this difficulty on to users when they try to make their own content. With a side-scrollers, you get a flat scroll to put stuff on that anybody can use. You can make a level for Megaman in a handful of minutes if you want, providing a much more viable and accessible user experience. This idea is the driving force behind the LittleBigPlanet game as a whole. Non-time-consuming content generation for many hours of ridiculous fun.