OK, this was on the main board for a while, but what the hey! Let's start a new one. It'd be best to mention an individual game rather than just saying "Gradius series" or something like that. I'll edit the list as we go along. You can mention systems or not.

Air Zonk (PCE, TG-16)
Axelay (SNES)
Battle Garegga (Saturn JPN, arcade)
Carrier Air Wing (Arcade)
Dodonpachi (Arcade, PSX JPN, Saturn JPN)
Einhander (PSX)
Gradius III (Arcade, PS2, SNES)
Ikaruga (DC JPN)
M.U.S.H.A. (Genesis)
Pulsar (Neo-Geo)
Radiant Silvergun (Saturn JPN)
Raystorm (PSX, Saturn as Layer Section II)
R-Type (Arcade)
Sonic Wings Special (Saturn, PSX)
Spriggan (PCE)
Strikers 1945 II (Saturn JPN)
Thunderforce IV (aka US Lighteningforce) (Genesis)
Truxton (Arcade, Genesis)
Twinkle Star Sprites (NeoGeo, DC, Saturn)
Xevious (Arcade, many home systems)