I'm strictly limiting my choices to games I personally love and recommend, and ideally, which version is the best available:
Arcade (MAME-playable)
- Armed Police Batrider
- Cyvern: The Dragon Wings
- Dangun Feveron
- Dragon Blaze
- ESP Ra.De
- Gekirindan
- Progear no Arashi
- Samurai Aces
Dreamcast
- Border Down
- Giga Wing
- Mars Matrix
- Under Defeat
- Zero Gunner 2
Neo-Geo
- Blazing Star
- Strikers 1945 Plus
PC
- Imperishable Night
- Perfect Cherry Blossom (really any Touhou shooters are great, though)
- Shikigami no Shiro III
PC Engine
- Ginga Fukei Densetsu: Sapphire
- Gradius II: Gofer no Yabou
- R-Type Complete CD
PlayStation
- DoDonPachi
- Gradius Gaiden
- Image Fight & X-Multiply
- R-Type Delta
- Raiden DX
- Sonic Wings Special
- Toaplan Shooting Battle
- Zanac x Zanac
PlayStation 2
- DoDonPachi Dai-Ou-Jou
- Espgaluda
Playstation 3
- Under Defeat HD
Saturn
- Batsugun
- Battle Garegga
- Cotton 2: Magical Night Dreams
- Gunbird
- Sengoku Blade
- Sexy Parodius
- Sol Divide
- Soukyugurentai
- Twinkle Star Sprites
Xbox 360
- Guwange
- Ketsui: Kizuna Jigokutachi Extra
- Mushihimesama
- Raiden Fighters Aces
plus a fair number that have been named already like Akai Katana and DeathSmiles