Tag-Team such as in Sonic Advance 3 and Sonic 4 Episode 2. I don't think either game used it to it's full potential, and I believe a truly great game could be built around it.
Sweet Spot Attack from Colors Ultimate. It makes the homing attack feel better than just a mindless button mashy way to destroy every enemy on screen by providing you with extra incentive to pay attention to the timing of your inputs, and in a way that doesn't come off as overpowered.
Lost World's Spindash. It's basically a meterless boost that provides slightly better handling, which sounds overpowered at first except it's also slower than the boost and takes a moment to charge up. Sonic as a character is more well known for the Spindash than for the Boost, and this particular implementation feels like the best compromise to me, at least out of any official title so far. If it allowed for more momentum/physics interactions like in the Adventure games, it would be much better.
Lost World's Parkour. While Lost World itself didn't handle this super well, the base idea is really solid and has a lot of potential for improvement. It reminds me a lot of the movement in games like Tomb Raider, Uncharted, and Darksiders 2, though much faster. If they could refine it to make it feel less unruly and give the player more of a sense of control, it would be ideal for exploring more open ended level design.
Lost World's Kick. While the multi-homing attack isn't really my cup of tea, the kick adds a really satisfying layer to defeating badniks by allowing some to be immune to the homing attack, or to allow chaining into other enemies by kicking them, or a number of other interactions. It makes attacking enemies far less brainless as you have to actually think about how you are going to approach a situation. I do feel like this move would be better for a future playable Shadow however, as it feels more in line with his personality.
There are just so many different moves and abilities to choose from, especially for someone like me who enjoys the classic games, the Adventure-style games, and the modern games. I think the best way I can choose is to narrow it down a bit and choose my favorite play style. In that case, my favorite is Sonic Frontiers. I love how it blends together classic moves with modern moves, and even adds some new flair of its own (like the great combat system)! I like that you have access to stuff like the dropdash and the spindash-esque counterattack moves, alongside the boost, stomp, lightspeed dash, double jump, etc. Sorry for the long rant....