One of the most well-known franchises in the world. It was one of the first games I ever owned (My father bought me a Sega Genesis when I was 4, complete with Sonic the Hedgehog 2 and Mortal Kombat....yes Mortal Kombat lol). These games are just so good. If you've never played a 2D Sonic the hedgehog game, you're missing out. I'd play a Sonic game over a Mario game any day (And I love Mario too, Obviously! haha). There's Sonic 1, 2, 3, CD, and Sonic & Knuckles. Sonic 2 is probably the best to start out with though. Sonic 1 is kind of difficult (no spindash), but Sonic two has it, and transitions to Sonic 3 easier (not to mention it has tails =D). If you play Sonic 3 you MUST play it plugged into Sonic & Knuckles. The games are incomplete without eachother (literally). When Sonic 3 was made, the developers were running out of time on production, so instead of pushing back the release, they released half the game in Sonic 3. Then months later, they released the other half as Sonic & Knuckles. Yes, these two games combined, are twice as big as Sonic 1 and 2. More levels, and 3 characters to choose from! The addition of the alternate path of Knuckles is a welcome one >=).
Also in Sonic 2, Sonic 3, and in Sonic 3 + Sonic & Knuckles, you can have a second player co-op as tails (if player 1 is Sonic). This is actually really fun, and can set up some hilarious moments when Tails goes flying off the screen.
The Dreamcast games are almost as good. Sonic Adventure and Sonic Adventure 2 are two really good games. Their only super duper flaw is the camera angles, but even then, they still aren't that bad. In Sonic Adventure 1 you get your choice of 5 character story lines that all have different game plays, it's a blast. In Sonic Adventure 2 you have 2 teams (Light and Dark). Each side has three characters that you alternate between that have different play styles again. This also gets rid of the two play styles from the previous game that were boring. When playing the Dreamcast games, just avoid "Sonic Shuffle" and you'll be okay.
The recent games have just been bad though (aside from the handhelds like the Sonic Advance and Sonic Rush series). Sonic the Hedgehog (the 360 and PS3 game) was just awful. As was Sonic Heroes, Shadow the Hedgehog, Sonic and the Secret Rings, and Sonic and the Black Knight. Terrible terrible terrible games. Sonic Unleashed brought back some 2D elements in "Day mode" but the "night mode" as a "werehog" was retarded.
Hopefully with the new release of Sonic the Hedgehog 4, I will be at peace lol.