I'd like to give a special mention to Armed Police Batrider, for having an incredible amount of hidden stuff and depth, along with being a brilliantly balanced shmup as well. It's also one of the few arcade boards I own, primarily because I love it, but also because the driver in MAME for all the Raizing games (Battle Garegga and Battle Bakraid being the more well known games from Raizing) has a small amount of input lag which totally messes me up.
Like all the awesome games in MAME, it's emulated in version 0.36 so it won't be on a handheld any time soon! Do yourself a favour and check it out some time!
Also, you can't really go wrong with any of Cave's games. Esp.RaDe (another one I own
), Do Don Pachi, Dangun Feveron are all brilliant. Guwange has it's fans, but I've never really gotten on with it sadly. Just as well, since it goes for big big dollar when it's on sale since it's so rare. While we're on the topic of Cave, make sure you avoid Do Don Pachi 2: Bee Storm - it's very much the black sheep of the series since Cave licensed it out to some Chinese company called IGS, who've yet to make a good game. Progear is another GREAT game, it's on Capcom CPS2 hardware since it was published by them, and sadly there are loads of bootlegs kicking around at the moment. It's also a horizontal shmup, very unusual for Cave.
Unfortunately, a lot of the Cave stuff is still unemulated. Do Don Pachi: Dai Ou Jou is brilliant (there's a PS2 version), Espgaluda is pretty good (PS2 again), Mushihimesama is also brilliant (far too new for MAME, but there's a PS2 version), Ibara - which I love but it widely disliked since it's more or less a Raizing game (PS2 version out soon apparently), and last but by no means least, Ketsui. I think it's one of their best games yet, but there's no home versions and it's not emulated.
And bringing me back on topic, here are some shooting games that are just great:
Twin Cobra (avoid Kyukyoku Tiger, the same game but unfairly hard later on)
Fire Shark (Toaplan pretty much formed the modern shooter)
Gradius series (although it kinda lost it's way a bit at 4 IMO)
R-Type (they're all good, R-Type Leo is a bit of a step backwards though)
Radient Silvergun (probably in MAME soon)
Raiden (the whole series is pretty good, 1st is a bit bland IMO)
Salamander (Lifeforce is the game with rubbish speech added, god knows why)
Parodius (I've not put any real time into these just yet, they seem pretty good though)
That'll do for now before I get into all the console games!
Edit: I spelled "Kyukyoku Tiger" as "Kyokyuku Tiger"