This isnt a SHMUP per se, but the Train level on ZOE II is very SHMUP-ish, imo. Other than that, I like the Metal Slug series.
Gunhed is my favorite shooter, pc engine game, and one of my favorite games of all time. This game is seriously the best thing to happen to the pc engine, and they seriously need a modern re-make.
Multibios? http://www.vsa-ag.ch/Services/STVDual/STVDual_e.htm I got one from them, and it's lovely. Get the EUR/JAP one if you want to avoid the irritating 'Winners Don't Do Drugs' message from the FBI Stone
I've had a bit of fun with RSG, when you switch to an American/European bios you get dumbed down gameplay, only two buttons and three, two of them modified weapons. Then there is the real treat, the intro in Engrish! I supose I could write it down and post it.
DoDonPachi for sure, followed by Blazing Star. I came across this rather interesting Japanese shooter for computer the other week called "Edoma". I only have the demo though and haven't been able to find anything at all related to it. I'd love to play the full version, but unfortunately I can't find anything on it. If anyone is interested in at least checking it out, I can post the demo up on my server for people to download.
I really liked Einhinder(sp) for psx. I think just because Square actually made a game that wasn't an RPG. Now that I think about it Tobal #1 was good for that reason too. All kidding aside both were really good games(Einhinder was hard as hell for me and I have yet to beat it). Silpheed gets honorable mention due to the fact that it was the only Sega CD game that didnt suck (I didnt have a PC back then).
arcades from my childhood. side arms. [discover the emu (mame) years later and realise just how insanly difficult it was....talk about cash vaccuum!!] a.s.o. notoriously difficult to complete. is it still? time pilot. nuff said.
While we're on it, I've gotta say i love Smash TV. I amost bought a cab for it about a week ago. And the everpresent nod to Radiant Silver Gun.
I had a lot of fun with Metal Slug 4 -- and I know that it's full of recycled visuals and incredibly linear compared to MS3 and whatever, but twenty five cents a credit at a (former) local arcade was such a good time. Actually, that same place had Dimahoo which was also enjoyable. Simple scoring systems are underrated (one of the reasons I can't get into a lot of Cave shooters (cough Dodonpachi cough)).
R-Type for me. The fact that an entire generation of shooters (even some modern ones actually) were referred to as R-Type clones (usually poor R-Type clones) says it all. Shooting perfection.
I go through phases of loving certain shooters, I used to love Ibara when I was in Japan, that was just bliss. I am a huge garegga fan though. It is just such a beautiful game in not a very obvious way, you just notice how special it is over time. That and the scoring system is great, in the way you can take it or leave it. Can't wait for the ps2 version, even if it is shit like mushihime, it will scratch the itch. At the moment I'm getting to grips with homura, not the best game, but exhilerating nethertheless (But I have never liked games with shield-esque systems that much). The music to that game is great and some of the set pieces are wonderful. I do find the scoring a bit simple but it is quite tough overall. I would recommend it, as it has a great visual style and is a solid ps2 conversion.