Surprised no one has mentioned yet: Knuckles' Chaotix for da 32x! This game is hit-or-miss for many people; however I generally like it.
Yes, although it is not exactly a cannon Sonic game (heck, it does not even feature Sonic as a playable character), the game does feature some interesting changes and unique gimmicks to the usual Sonic Game formula, including 5-Act Zones, a Daytime system, the combi "buddy system", the Chaotix team as players each with special abilities, very colorful graphics, new TV powerups, full-3D Bonus/Special Stages, a rocking soundtrack, no-lives, and the adventure-based gameplay style with random stage selection and the Newtrogic High Zone home world. The 5-zone system and level layouts aren't meant to be rushed through like in most Sonic games, and allow players to enjoy the atmosphere of the zones and explore adventure-style, and the co-op system makes the game more playable for 2P, instead of Tails lagging behind and getting beat up like in Sonic 2 & 3nk. The game also has its Tutorial Zone in order to teach new players how to use the combi system.
The only thing I don't like are the layouts of the zones: many are quite empty and feel somewhat rushed. The dev team had good ideas, but it was not entirely executed very well. Despite this, the levels include many interesting gimmicks, such as the whole "turn on the clock" thing in Amazing Arena and mini-boss, the floating ship chunks in Marina Madness, the door, switch, and elevator gimmicks in Botanic Base, Speed Slider with its fast slopes, and Techno Tower with its conveyor belts and vertical-based levels instead of Sonic's usual "press right to win" type of levels.
Somewhat off-topic, also the fact that the game has almost as many prototypes floating around on the interwebs as Sonic 2 (and even having a separate tech-demo, that Sonic Crackers game) makes it worth looking into rom hacking-wise for a programmer/game dev like myself. Although SonED2/Romulan is the only utiltiy available ATM to edit level layouts, no one to my knowledge has yet made even an attempt at a full rom hack (SH-2 asm edits aside), and I wish someone would give the game more luv :(. While playing around with SonED2 and documenting object definitions, IIRC, in either the Introduction Zone or Training, one of the acts has a path swapper object which could be used to make better levels with multiple paths and loops. (Some of the protos have loops).
Although for some, its deviation from the standard Sonic formula makes it too radically different, I like the changes from the norm.