This is an ambitious topic, but I'm working on a rather ambitious project - the Contra H.Q. is going to expand into other game series as well. The criteria for inclusion, loosely defined, is that it has to be a single character, on foot or flying (because we don't want to exclude Battle Mania), and the focus has to be on shooting (and sometimes throwing, 'cuz that'd knock out some legitimate shooters as well such as Toki or Mystic Warriors), though Ghosts'n Goblins would be excluded as it's already got its own fansite.
If it's a spaceship, I can't count it for the same reasons. Kinda strange way to classify things, but this should give coverage to a wide selection of games that have gone relatively uncovered up to now (aside from the occasional classic gaming plug or what have you).
Edit: Yes, that's rather vague, isn't it? Well, it might help to think of it this way: It should have gameplay very much similar to a gameplay style seen in Contra. That means sidescrolling run and gun games are in; top down (Commando style) games count, and third person ones as well (not just because of the PlayStation Contras - think of the corridor sequences from the first Contra).
Here's a number of shooters, and my thoughts on them:
Contra (NES vs. arcade): The arcade version is awesome. For one, the bridge is easy to get across...The more time I spend with it the more tricks and patterns I learn. Its shortcoming is that it's far too short, especially in the later stages - the Ice Field is roughly a football field away from the end. Too short! I haven't tried out the higher difficulty levels, however. There's also an MSX2 version of the game, notable for its excellent manual with detailed diagrams of the weapons, drawings of enemies, and a map of the entire island from two perspectives (top-down, and from the side)!
Super Contra (arcade): Currently a favorite. Contra did well not because it was such an original concept - though the omnidirectional shooting was pretty new, even that had been done before - but because it was polished - and the graphics! The hodgepodge of weapon icons and silly looking weapons from the first arcade game are totally gone, and every weapon now gets its own sleek looking item drop. Shot animations are amazing, and I like the little flashing lights affixed here and there to the characters and their weapons (see the Super Contra flyer for this idea gone awry).
Battle Mania/Battle Mania 2: TS Vintage: One of my other favorite series of all time, but unfortunately limited to only two games. The control scheme is not nearly as unwieldly as it could've been, and lets you direct fire in two different directions at the same time with relative easy. You'll indirectly control up to three characters in the first title when a hostage becomes an ally! The sequel sports a rockin' soundtrack and much improved visuals along with one of the most humorous sound test interfaces I've seen yet Lots of humor (even silly gaijin like me will pick up on a lot of it) and all the action you could want.
Toki/JuJu Densetsu: I don't think it fair to discriminate against apes simply because they throw stone axes. Toki's a cult classic (I actually followed an eBay auction for the PCB a few days back, so I feel that's a fair statement) with great, if quirky, gameplay. It's vaguely like Chelnov, which is to say vaguely like playing Super Mario Bros. with a fire flower. Here the emphasis is on hitting everything that moves enough to knock it out. Remember: You must keep playing or I'll die [not ME, Toki's girlfriend, silly]!!! Most pathetic continue feature ever. Got a port to the Mega Drive and Genesis as "Toki: Going Ape Spit" in the western hemisphere; the Japanese version is simply "JuJu Densetsu." One of TAD's best games.
Chelnov: What's there not to like about this game? It's got the hammer and sickle of the Soviet Union right there with the Statue of Liberty, for cryin' out loud! A cheesy (but well-done) comic book intro gets you into the arcade game. The Genesis port suffers a bit from its rather ugly cinematic intro, but sports some nifty background graphics. Racing pyramids! Chelnov (Nuclear Man, The Fighter!) should please both platforming and shooting fans.
Xain'd Sleena: Very pretty Sammy game, with a nice control scheme that allows double jumps and shooting crouched or prone quite a while before Contra did it. It does suffer a bit from the straight-forward shooting only, as even with options such as an arcing grenade launcher enemies will tend to hover just out of reach of your weapons. I don't much care for the secondary shooter mode, but all said this is a great game.
FixEight: You can check out the bootleg in MAME, but the processor is only running at 5/8 the speed of the real unit, and it's missing a yamaha sound chip. It's a testament to the game's design that despite these shortcomings the bootleg is pretty enjoyable. Fixeight is Toaplan's successor to Out Zone, and while I don't believe the locations to be quite as interesting as Out Zone's, they're pretty close. There's some fantastic enemy mech design to see here, and the eight selectable players all are worth a shot. I never knew robots could scream until I played this game
Out Zone is amazing as well, and here's a great link for it: click. Great site, even if he does call Out Zone the "Sci-Fi version of the popular "Ikari Warriors" from SNK."I've found a Japanese FixEight fansite, as well, but don't have the URL handy.
Speaking of Ikari Warriors - you're familiar with SAR - Search and Rescue by now, right? I've always liked this game, but to be honest it's too easy and the whole thing's a bit of an ugly mess (especially non-human enemies). Despite the too-powerful weapon system (powering up shots annoys me, however), it's still a blast to play.
Ninja Emaki: One of my favorite games. MAME describes it best: think Commando, with a more interesting playfield.
There's many, many more games, but that's just a sampling of what's on my mind. Some other games to look out for:
Ninja Commando (Neo Geo, MVS/AES/CD)
Ninja Spirit (I wonder, Legend of Kage is a near fit as well)
Cyber-Lip (and, of course, the Metal Slug series)
Psycho-Niks Oscar (inspiration for the Turrican series!)
Soldier (Game King; see Brian Provinciano's site for a review and screenshots)
...and many more.
I'm still wondering whether the Dynamite Duke/NAM 1975/GI Joe/Cabal style game could be counted as having gameplay similar to the isometric corridor sequences from Contra...if I have my way they'll be :P
Feel free to add your thoughts!