A MegaCollection Kits
★ marks things I personally have played and recommend. Please let me know of anything else I could add in the comments at the bottom.

One of the greatest Sonic fangames of all time, built on Doom Legacy
Main Website Forums Server Browser
It is recommended that you create an account on the forum before you download anything in order to follow the mods for updates.
Utilities
LauncherBlast2 reBoot for easier mod-loading. SRB2 Uncapped for smooth FPS. SRB2 Uncapped PLUS does that and Discord Rich Presence. Custom gamedata to save with mods enabled. A VR mod also exists. srb2dl is a command-line download manager. srb2srv is a CLI server browser. srb2bld can help compile alternate builds of the games (as shown below).
Alternate builds
SRB2 Uncapped PLUS boosts the framerate with interpolation and adds Discord Rich Precense. Moe Mansion adds that for SRB2 Kart (below), as well as a better character select screen and camera tilting. SRB2Kart Galaxy does this for the more recent Kart version. SRB2NetPlus removes control lag when playing online. rphys overhauls the physics engine and gives the base characters new moves. SRB2 VR Mod and Sonic Kart VR Mod add VR.
Other Websites
Mods
Too many to reasonably count.
Maps
All Official Level Design Collabs ★ (formerly Contests). Also see the Unofficial Level Design Collabs (Link to forum member that hosts them) ★.
The Mystic Realm (Old Site) ArchPack Sol Sestancia SSNIsland Chaos Domain Logarithmic Train Zone Angel Island Tour ★ Island Tour Dimension Glaber New Horizon Neo Palmtree Zone Equinox Sonic 2006 SRB Dream Emulator Sweet Bro and Hella Jeff - the moive
Gameplay
The True Arena Snolf Super Run SRB2Randomizer Chaotic Edition VS. Metal Mode Paintbrush Sonic Paint Blast 3D foxBot Day/Night Cycle (Works with Werehog below)
Cosmetic
Jeck Jims' 3D Models Mega Paint Drive H-SRB2
Characters
Tweaks to Vanilla Roster
CrossMomentum MetAlt V. Maximum Overdrive
Alternate Versions of the Base Roster
Xtreme Junio Sonic Adventure Sonic Modern Neo Greeneyes Sonic New Bandages (Sonic Boom) Earless (SRB1 Sonic) Super Sonic Crystal Sonic Super Mystic Sonic HMS123311 Alt SSN Sonic Hard Sonic OVA Knuckles Chaos Knuckles Ugly Knuckles Plug-Hand Knuckles Amy Rose Pack Rose Gold Amy Magic Metal Sonic ChrispyChars (Pointy Sonic, Fluffy Tails) Max Control Pack Overhauled Legacy Trio (Hand Drawn, Less Unique, Chrispy Marriage)
Other Sonic Characters
Eggman (Eggpack) Egg Robo Mecha Sonic Sonic R Characters (Metal Knuckles, Tails Doll) Bean Honey Shadow Silver Blaze RushChars (Blaze, Marine) Espio Werehog Advance Cream Tangle Whisper Surge
Crossover
Kirby Meta Knight Elfilin Super Mario Bros. (Mario & Luigi) Bowser Yoshi Kamek Pac-Man Spyro Duke Nukem Kiryu Kazuma Cacodemon DeltaChars (Kris, Susie, Ralsei) Bubsy the Bobcat Meat Boy Plague Knight Windows The Kid Among Us Impostor Henry Stickmin Pig from Angry Birds Taz the Tasmanian Devil FL Studio Chan
OCs
Sonic.EXE Eggette "Omelette" Robotnik Maimy Team Kinetic (Dirk, Whirl, Vesola) StephChars (Skip, Jana) Gemma Nasya Wido Flame Ivory Willo Feels HorizonChars (Milne, Iclyn) Cacee "Kiwi" Cactus Piroli the Butterfly The Derp Wheelchair Inazuma
Multiplayer
Not needed unless hosting or playing singleplayer/locally.
Modes
SRB2 Battle! (BattleMod) Chaos Mode Pizza Time (Alternate take)
Exe Survival and Exe Terrorism come with Sonic.EXE (above).
Gameplay
Coop or Die! The Special Minigames
Maps

Total conversion that turns the game into an FPS with a new campaign
Character: Samus Aran
Multiplayer: Hunters

The ultimate racing crossover
Mod Link Server Browser
Moe Mansion for FPS boost, better character select, and server browser quick join support. Nyoom Launcher, Jeck Jims' SRB2Kart 3D DLC, and Community Models are also suggested. Player Bot Mod is an alternative to joining online. A VR mod also exists.
No addons are really needed unless you want to host you own server. Or to play them in singleplayer/locally.
Maps
Kart Rev Masters Pack Nightmare Pack Abstraction Pack Chengi's Track Attack Pack Aparte Cup Slipgate Cup
Tweaks
KartMP Juicebox Hitfeed Driftboost Gauge HORNMOD
Gameplay
Chaos Drives Wipezones Team SRB2Kart Racing FRIENDMOD Paragliders ChaosKart Elimination Weathermod Battle Plus

It's a JRPG with multiplayer now
Mod Link
Some characters have Persona support.

Now it's like an MMO in the style of Phantasy Star Portable 2 Infinity. Complete with Symbol Art.
Mod Link (Or just join a server)
Make
Zone Builder to make maps. Lua for scripting.
Find More
The forum hosts all the addons, sorted by top and featured.
Background taken from official site.
Suggest more in the comments!