If it wasn't the first side-scrolling platformer, it certainly introduced the genre to the masses! It was a cute, whimsical, family-friendly game that was very slick in every way (programming, graphics, music).
The mirror-smooth scrolling demonstrated the NES' superiority over the previously-dominant Colecovision, which had clunky-scrolling games.

It may have been the first game of its kind to introduce "secret" rooms, levels, and items, rewarding experimentation and exploration. I can't think of a arcade/console game that tried that before.

It also was the game that really cemented Mario as a "star." Even though he was featured in previous games, he was overshadowed by Donkey Kong. The "Mario Bros." arcade game (not Super Mario Bros.) introduced many of the basic game mechanics featured in the SMB series, but Mario was paired with Luigi and didn't really stand out, personality-wise.

That said, SMB really didn't grab my prolonged interest. I enjoyed SMB II MUCH more. SMB2 had slicker graphics, a wider variety of enemies, and what really got me were the "Boss" battles, which were very cool and creative! Even though SMB2 was not originally designed as a Mario game (it was actually a retooled "Arabian Nights" themed game), I found it a much more attractive Mario game.

SMB2 also represents a break from the "arcade" roots of Mario in that there apparently was no score! Your motivation was completing the quest, not racking up points! This was a true "home" arcade game that allowed you to take your time and explore the world.

SMB3 seemed to go back to the first SMB game in that it reintroduced the scoring and most of the game mechanics of the first, so it was actually the true sequel to SMB. Therefore, I didn't like it as much as SMB2.

The modern console Mario games seem to be inspired more by SMB2 than the others in that they are quest-oriented as opposed to score-oriented.

Sega's "Sonic" games never grabbed me at all. The levels seemed complicated and aimless. Where the heck was I supposed to go? Left... right... up... down? Oops, I went down, now I can't go back up again and collect the rings I missed! Man, now Sonic is running at 500mph, but the level's whizzing by so fast I become disoriented. It was a "hardcore" platformer that lacked the more straightforward (literally) goals of the SMB series.

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