There's so many!
Some of these may have been already mentioned.
I've split it into Arcade and PC Engine.
[Arcade]
R-Type (series I, II)
- Early scroller, very impressive. Huge ships. Great playability. Love the power ups.
Scramble
Gradius (series I, II, III, IV)
- Classic power up. Scramble was the fore-runner to Gradius. I love all the Gradius, I and II and probably my favourites.
Parodius
- Parody version of Gradius. Also a 'sexy' version with really pretty cartoon graphics.
Twin Cobra
Raiden (series I, II, DX, Fighters)
- Probably my all time favourite vertical shooters. Twin Cobra and Raiden are just the right balance of shooting, dodging, difficulty and power-ups! And such a shame when you die and you see all your power-ups disappear! Though you could catch some of them floating around in front of you. The PC (not "PC Engine") version of Raiden II is awesome!
Choplifter
- Based on the classic computer version, this is the definitive version for me. Great color graphics. Perhaps not a pure shooter but I always love playing in. The Sega Master System version is highly recommended.
1941
1942
1943
- Classics. My favourite is 1943, fantastic frenetic shooting, with extraordinary pretty graphics for the time. I loved the parallax effect and particularly loved experimenting with the weapons.
Most people probably know 1942 (chronologically the first produced) and possibly dismiss 1941. There's also 194x and some other later variants but I don't really rate those.
Dragon Spirit
Dragon Saber
- Nice vertical shooters with power ups.
Dragonbreed
- Another great shooter, a bit slow but the dragon power ups were novel.
[PC Engine]
Gunhed
Super Star Solder
Final Soldier
Soldier Blade
- Awesome games. The PC Engine was a sprite monster and these games proved it. They are a nice combo of power ups and just plain fun shooting. Perhaps a bit easy, especially when you are fully powered up.
Soldier Blade has awesome graphics. Final Soldier allows you to choose weapons before starting.
Sylphia
Spriggan
- Pretty graphics and not a bad shooter
R-Type
- Deserves a mention on the PC Engine for being an example of an excellent conversion.
Galaga 88
- Sort of scrolling. Classic Galaga with extras. Everything you want for a sequel.
Atomic Robokid
- A bit easy but big impressive visuals and nice gameplay.
Mr Heli
- Cartoony and fun but quite a good shooter, where you collect coins to buy new weapons of your choice.
[EDIT]
Star Parodia
- Cartoony parody of Super Star Soldiers using your choice of bomberman, pc-engine or <some other> character. It's really nicely presented with lush graphics.
Ai Cho Aniki
Cho Aniki
- I'll get totally bagged for adding these in, but they are good shooters in their own right even if their subject/content is questionable.
Steam Hearts
- It's okay, possibly a bit hyped and definitely overpriced for what it is. Has some nice cut scenes though, but then that's not what a 2D shooter is all about, right?
Gradius II
- Like R-type, special mention for Gradius II on the PC Engine. Amazingly good considering the PC Engine specs.
Gate of Thunder
Lord of Thunder
- Some people rave about these ones but i'm not convinced. Something lacking to make them truely excellent in my opinion but still worth of mention.
Macross 2036
- Excellent, especially if you are a fan of Macross(J)/Robotech(US). Side note: I have both Macross and Robotech DVDs; do yourself a favour and get the Japanese version!