Sonic The Hedgehog: Chaos
aka: Sonic Chaos

Level select:
Press Up(2), Down(2), Left, Right, Left, Right at the title screen. Then press 1 or 2 to select a new starting level.

Invincibility:
Select Sonic, then hold Up and continuously jump. Eventually Sonic will begin flashing. Note: The invincibility will end when Sonic stops running.