Like many others on this thread, my favorite ROM hack is without a doubt Sonic VR. The hack single-handedly proves the saying "Sonic is all about speed" wrong. While it is partly his own fault that Sonic has this saying latched on to him (due to the branding), nothing suggests the opposite as tremendously as Sonic VR. Although it is only a short 40-levels obstacle course, it sheds light on the nuanced gameplay that can be accomplished with the physics in place. For example: In one of the levels, you'll be jumping from platform to platform while getting attacked by buzz bombers. At first, they're a nuisance, however, skilled players will quickly realize that with good timing and aiming, the buzz bombers themselves become platforms which can be used to create a path towards the goal. In a later level, the player has to run up a wall and eventually the ceiling which has several slopes that increases in size. If you run too slow, you fall. If you run too fast, you also fall. The player has to balance and control the speed to make it to the goal. Such things and many others were never fully explored in the classics. Megamix v.3.0 did this too and incorporated it in a smart manner. In Dark Fortress Zone, hidden item boxes were scattered all over the level but to receive them, the player would have to complete a puzzle using the physics or mechanics of the classic Sonic games (like bouncing from item box to item box over a pit of lava). You can also find such level design in Sonic Alt. It's just too bad they are usually over a bottomless pit.
Favorite fangame? Sonic Utopia. It's gonna be great! I hear that they're contemplating on adding Sonic VR-like challenges somewhere down the line. Even if they don't, just the thought of them considering it makes me have that much more faith in the project.