In Sonic 2 and its two direct sequels, having all 7 Chaos or Super Emeralds and at last 50 rings when pressing A, B or C in the air causes Sonic (or Knuckles (or Tails is all Super Emeralds have been gathered)) to transform into their Super or Hyper form.
In Sonic 3 & Knuckles and Sonic Advance 1, 2 (and 3 with some character combos), when pressing the A, B or C button in mid-air you produce an "Insta-shield" (or if you have a shield equipped, a different move).
In Sonic Blast and Sonic R, pressing the respective action button causes Sonic to do a double-jump.
All 3D Sonic platformers make the blue blur do a "Homing Attack" when pressing the jump button in mid-air.
In Sonic Battle, the push of the A button in mid-air causes a small forward acceleration (the name I have forgotten), and Sonic Advance 3 has a few different things that might happen.
Ah yes, in Advance 2 (and from what I've heard also the Rush titles), pressing A in the air near an enemy will also cause a homing attack.