Gradius - Well, it's the first of it's kind so....it started the whole series.

Gradius 2 - Allowed the player to pick between four(?) different weapon setups.
Gradius 3 - Introduced the Weapon Edit Mode.
Gradius 4 - Ummmm....the first Gradius to use polygons?
Gradius 5 - Where we are at today. Gradius V incorporates elements from Salamander series (instant respawn and 2p co-op), but adds new stuff as well, such as a small hitbox and option control.