In the Sonic the Hedgehog series, Super Sonic is the transformed state of Sonic when he has all the Chaos Emeralds. Getting all of the Chaos Emeralds is quite a feat in itself - the player must pass through several special stages, which may or may not be easy to find; there are a limited number of chances to enter the special stages within each level.
Super Sonic was introduced in Sonic the Hedgehog 2, and subsequently Sonic 3 & Knuckles. In Sonic Adventure, Super Sonic is available at the very end of the game. Sonic CD features Time Stones, not Chaos Emeralds, so no transformation is possible. In Sonic Pocket Adventure and Sonic Advance, he's available at the end of the game too.
Once the player has all of the Chaos Emeralds, becoming Super Sonic is easy enough - just collect 50 rings and jump in the air. Interestingly enough, he bears a remarkable resemblance to a Super Saiyan. Super Sonic runs extremely fast, can dance a jig on normally lethal spikes, and take down a boss with extreme ease. A few caveats exist in this form, though - our hero Sonic is still vulnerable to drowning, being crushed, and falling into a bottomless pit. Also, like a crack addict, the player must sate Super Sonic's addiction for rings; he consumes them at the rate of 1 ring per second. When Super Sonic runs out of rings, he reverts back to Sonic the Hedgehog.
In Sonic 3, a sort of upgrade is available - Hyper Sonic, available when the player collects a second set of Emeralds. Hyper Sonic moves even faster than Super Sonic, and can kill everything on the screen, save bosses, with his super move.