Xevious - Frankly, I was surprised how much I grow to like it. But I also like Zanac, so maybe it's not that surprising after all... My favorite way to play it is via the PCE IFU: I put a CD into the tray and listen to electronic music through earphones, while still hearing the special effects of the game in distant resound. Hehe, love it!
Darius II - The most atmospheric title. Period. I wish, that I could play it extensively on a dedicated three screen cab, but as of now, my favorite version is the Mega Drive one.
Zanac - This one is pure adrenaline. I love every single Compile STG, but if I had to take just one on a desert island...
Galaxy Force II - Thanks to the SEGA AGES 2500 I could catch up on this gem on my PS2. It's like Star Wars entirely drawn by Moebius. The alternating feeling of weightlessness and thrust, when you pilot through fanciful planets filled with lava streams, waterfalls, labyrinthian caves and tunnels is captivating. It's also so short, that you can pop it in anytime you want. Classy game!
Hellfire - A personal fave, maybe because it's so rigorous and simple like a, hmm... a cliché'd German? Well, I'll skip the denial part.
X-Multiply - Just wanted to be original with this one, so it's mentioned here instead of R-Type. I'd also like to mention, that my most favorite R-Types are those not made directly by Irem: Last Resort, Viewpoint, Pulstar etc. That's not the 80s, though. Which reminds me: I hope this thread gets a worthy sequel.