1. Shadow the Hedgehog
https://mb.srb2.org/addons/shadow-the-hedgehog.517/
The chaos snap is a very fun move, especially once you get the hang of it. (Let go of the movement keys to aim it upwards.) Be warned that he *does* say "d**n" sometimes, unless you turn off that easter egg.
2. Adventure Sonic
https://mb.srb2.org/addons/adventure-sonic-v1-6b.3589/
Spamdash, ledge grab, bounce... it's all here. Possibly the best non-vanilla Sonic of the ones I've tried. Certainly more powerful than vanilla Sonic, but still feels fairly balanced for the vanilla campaign.
3. Super Mario Bros.
https://mb.srb2.org/addons/super-mario-bros.3420/
Very complex moveset, but mastering it will let you pull off all sorts of crazy moves. Chaining together wall jumps are an especially powerful tool once you learn how to pull them off consistently, and the power-ups are all quite fun. Bosses are noticeably more difficult however, due to the different health system, however.
4. Modern Sonic
https://mb.srb2.org/addons/modern-sonic-v5-12.501/
Overpowered and rather unbalanced for the vanilla campaign, but very fun nonetheless.
This is far from a comprehensive list of great mods, but these are the ones I've played around with enough to personally recommend. Some others that look promising (but which I haven't tested out much yet myself) are Bandages, The Chaotix, ChrispyChars, Eggpack Remake, Greeneyes, Kirby, Max Control Pack, Neo Sonic, Pig, S3 Sonic, Silver, and Windows the Computer.