I decided to type up a little snippet for each game in my list. Hopefully I won't regret it.
Mars Matrix:
Just by far my favorite game ever. I could probably go into a lot of detail about all the little touches in each of the stages, but I'll try to bring up the most significant parts. The coolest element is, of course, the mosquito system. Not only can you use your opponents firepower against them, but, unlike other reflectors you actually have an incredible amount of control of the direction that you send the bullets. It certainly take some getting used to, but is well worth it, IMO.
Apart from the control, I really like the way that the gauge functions. You can drain it any amount to pick up bullets, and it will become full again faster depending on how long you use it for (because it refills at a constant speed). This gives you a lot of flexibility. Just need to clear a little space out in the bullet patterns? Just tap shield. Want to get the maximum possible gold out of a boss' bullet spam? use the shield as long as you can without triggering the Gravity Hole Bomb. However, you always need to wait for the gauge to refill all the way (unlike in RefleX, or Samidare). This forces you to plan out your shield use a little bit, especially when you need to go for longer-duration shields. If you hold it down for too long you get the Gravity Hole Bomb which can really screw you up, especially if you're trying to score. This forces you to get a feel for the shield gauge in order to succeed.
Additionally, MM has really excellent pacing. The first couple of stages are easier, but also really short so they never feel like a drag. The total game length is only about 18 minutes. Just about perfect, especially given the intensity of the game. There's probably more things that contribute to the pacing, but it's definitely among the best paced games I've played (up there with Psikyo stuff).
Also, The bullet patterns are really fun. as PCEngine Fan X once said (paraphrasing) "Takumi style scattershot patterns." There's a lot of big clumps of bullets, clumps that spread out as they move across the screen. A lot of walls of bullets. The more micrododgy patterns tend to be sparse spreads of bullets across the entire screen. Stage 3 has enemies shooting out arcs of bullets that form a maze. Choose the fast ship and you'll find yourself actually weaving around them on the screen much of the time. Very intense, and perfectly designed around being able to reflect bullets against enemies to make medals, as well as ships that don't have a focus (I find myself increasingly not really enjoying playing games that have focus mechanics).
Last but not least there's the scoring. Timed medal chaining. Fill in the gaps in the chain by reflecting bullets into medals. This will allow you to build up a multiplier which basically ends up getting cashed in in the final stage where you have lots of high value enemies to mow down. Easy to understand and yet incredibly deep. Mars Matrix is probably the only game I will ever seriously play for score.
Giga Wing 2:
Only recently started giving this game a fair try, and it's very quickly made its way up to near the top of my list. Similar patterns and pacing to Mars Matrix, but more boss focused (and the bosses are quite fun). I don't like the reflect mechanic quite as much as the MM one, but it's probably a close second. Scoring is based upon getting the immensely viscerally satisfying "volcanons" where, if there's enough medals on stage at once they explode into more medals. Not too much more to say on the matter
Gunbird 2:
This was one of the first shmups I bought when I first got into shmups. I spent many hours grinding trying desperately to figure out how to get through the fourth stage (sky stage, I think they call it), and failing. Alas, it was way above my skill level at the time, and probably still is (especially since I still suck at using smart bombs). I think what I like about it is the breakneck pacing, the melee attack focused gameplay, and the fact that very often it's safer to be near the top of the screen and take out enemies before they are a threat (or in some places seal their bullets). There's probably more to it, but I haven't played it as much since I stopped having an SDTV (It doesn't work with my vga-only PC monitor, and I haven't found a character in the arcade game in MAME who I like quite as much as Morrigan in the DC version)
Zero Gunner 2:
Classic Psikyo pacing and patterns, but a slightly more forgiving difficulty. The actual appeal of this game is largely in the fact that you can rotate your ship around. For whatever reason I find this weird "hold a button to rotate" gameplay a little easier for me to wrap my head around than, for example, a twin stick game. That's about all I can say about it. It's a super well crafted game, and very fun.
Samidare:
This is another reflect 'em up, except it actually isn't. It's like a pseudo-reflect 'em up. Instead of literally reflecting bullets back at the enemy, The reflector absorbs bullets and turns your shot into a more powerful, x16 point shot. The more bullets that you absorb the longer the powerful x16 shot lasts. That pretty much sums up both the gameplay mechanics and the scoring. It's very simple, but actually quite deep from what I've seen in other people's replays (I never got that great of a score). The extra stage seems like it's both harder and deeper, but I haven't spent a lot of time with it. I actually think that this gameplay mechanic is super fun, and interesting, and I assume a little easier to program than a traditional bullet reflect, so props to RebRank on that. Apart from the gameplay mechanics, the game is very boss-focused, has super fast pacing, and is very intense. Really fun bosses as well.
rRootage:
This game is on my list because I would be lying to myself if I didn't say that I've had a lot of fun with it over time. The bite size challenge structure may not be quite as satisfying to complete as a whole 20 minute arcade game, but there are times when I can't get into the idea of practicing a stage or playing a full credit of an arcade game, and just want to react to patterns (often random patterns), and see how long I can survive without bombing or whatever. In addition, the game has 4 modes with different mechanics each with something like 40 stages that can be separated into 10 difficulty levels. one stage in each difficulty of each mode is randomly generated every time you play. It's good stuff.
R-Type:
When I first heard about R-Type, I was like "bullet soaking, that sounds lame," but now that I've actually played it (1-ALL'd it, in fact) I realize it is a tactical shooter of high calibur. The force gives you a lot of interesting options for how to tackle the stages. The stages are well designed, and the boss quick kill and / or safe spot strategies are really fun to pull off. The only downside is that some of the time the power ups are your enemy, and it's not really possible to recover past maybe like the second stage. I will say that there are more frustrating games when it comes to power up dodging, but R-Type is definitely a product of its time in those ways. I really must try II and Delta one of these days.
Dangun Feveron:
I haven't spent that much time with this game, but from what little experience I've had it is incredibly fun. fast, sparse patterns, caravan-style bonus enemies, and discoman chaining (which has got to be one of the better scoring systems ever devised). Possible down sides are that it might be a little long for how difficult it is, and maybe just more difficult than I generally like in a game. The ship is also real twitchy if you want it to be fast enough, but at least the bullet patterns are designed around that.
Fantasy Zone II: The Tears of the Opa Opa:
Best 3DS shmup, probably, though, because I value my thumbs, I usually play it in MAME. This is a game that also seemed pretty unappealing to me when I first heard of it, especially with the shop system, two-directional scrolling, and potentially brutal recovery, but actually, once you introduce autofire and trying to get through the stages fast it turns into a very nicely paced game with pretty reasonable recovery (They make it very easy to get speed and double bombs back, and that's all you need for most of it, even if the fire bomb makes things a lot easier). Light and Dark stages allows for you to play the game at a difficulty that feels more reasonable to you. Also gets pretty intense in later stages even on the light stages, though probably never to memo requiring degrees (though I haven't played the dark versions of most stages). Pretty original and fun boss designs as well.
Tumiki Fighters:
Kenta Cho's only game that plays like a regular shoot 'em up instead of being either bite size challenges, or endless stages, or both. In addition to standard and solid bullet patterns, the enemy catching mechanic is very unique and allows for some interesting and fun strategy. Gets pretty intense when rank gets high.
Under Defeat:
Brutal tactical shooter that is very intense and full of viscerally satisfying explosions. Boss quick kill strategies are quite fun. Planning ahead with where to launch your rockets is what it's all about. Maybe a little bit on the slow paced and long game length side, but overall a very fun game. I promise I'll clear this some day, Stevens!
Eschatos:
Wasn't sure whether I should include Eschatos or Judgment Silversword in my list. JSS is better paced, IMO, but playing with the standard ship it's almost required that you use the button-mashy hybrid shot strategy, which my thumbs really don't appreciate. Both games have pretty interesting weapons systems, with a very cool shield mechanic that is unlike any other that I've seen (though IMO not in the same league as Mars Matrix. Note also that you don't need to wait for the gauge to recharge to use the shield again in these games, which is not necessarily a bad thing, but is something that I really like about the Takumi games. Also there is not bullet reflecting in either of these). I think what I actually like most about Eschatos (and JSS) is the pattern design. Hard to describe it, exactly, but MKai / Qute makes some fun bullet patterns. Another thing that stands out in Eschatos is the rotating stage hazards in stage 3. Those things are cool as fuck.
Triggerheart Exelica:
This game has a weird kind of mystique to me, as I remember hearing about it being released on the Dreamcast many years after the Dreamcast had fallen out of pop culture (maybe a little bit before it came back into the pop culture in a nostalgic way, though I don't really remember that well). At the time I was still playing the DC, though I don't think I was playing many video games in general in 2007, but DC was my only system. I also was probably unaware of all of the other post-mortem DC releases, though I was aware of the homebrew scene as it pertained to emulators, mostly. I certainly knew nothing about the gameplay (not sure why I never looked up video footage of it, though). Anyway, the name stuck in my head, and it was cool to finally be able to get it affordably on XBLA. I only mention this because I don't know if I would like it as much without that mystique.
It is, however, very original in gameplay mechanics, and very fun, especially with autoswing off, which allows you to choose whether to swing or just to use enemies as a shield, even though most of the time you just want to swing, and it can sometimes screw you up to have the manual swing. Being able to anchor onto ground enemies and bosses and shoot a directed attack at them is also a very cool idea. Anchoring onto enemies slows down your movement, too, so focused shot is wrapped into this one cool mechanic. Stage design is very well done for using the anchor, and bullet patterns are generally well done, and sometimes even a little fancy. They're more curtain fire type patterns than most of the games on my list.
Valkyrius:
Valkyrius kinda seems bad in theory with a warp mechanic and ammo-limited powerups, but there are enough patterns that are designed around the warp to make it feel necessary, and not so many as to overwhelm the game. The warp also seems very well implemented with two different distance choices, and a circle drawn around your ship to show you exactly where you'll end up. It's actually pretty fun to use. As for the power ups, I think you're default shot is adequate most of the time, and you can really play the game without worrying about conserving ammo so that is okay. What really shines about this game is actually the patterns, and maybe also the boss fights. Patterns are fun in a similar way to Eschatos patterns to me, and there's a few non-bullet hazards that are cool, e.g. the enemy shockwaves (Gotta warp past those!).
V . V:
Like Dangun Feveron, I haven't really played this game as much as I ought to before voting for it, but I do quite enjoy the bullet pattern style of late Toaplan games (including Cho Ren Sha, even though that isn't a Toaplan game). This one is the one that felt the most enjoyable to me, though, for whatever reason. I also think it did a good job of implementing a Gradius-style power-up system without making recovery impossible. You can always get that one speed up and the default level 1 weapon is decently powerful