Espalion (PC)

Espalion is a shooting game made in 2004 by a Japanese indie developer named Team DRYUAS, and as far as I'm aware, it's their only work.
It feels really different to most shooting games, and though at first I couldn't put my finger on how, I eventually realised that playing Espalion feels less like flying a fighter ship in a future war and more like taking part in some kind of choreographed performance. The enemies are all arranged into exact positions, and have exact lines of fire to create intricate grids and weaving patterns, in contrast to the chaotic spirals and shapes of typical shooters.
The way it plays is fairly unique, too.Your main (and only) weapon is a pair of two shields that shoot streams of bullets, either in front of and behind your ship, or to either side of your ship. You switch between the two positions at the touch of a button. The shields also absorb bullets, which is also the game's main scoring gimmick. As I said earlier, the game feels like a choreographed performance, in which you're expected to find the right place to be to survive, as well as the right alignment for your shields to both absorb enemy shots and kill those enemies.
The choreographed feeling doesn't hurt the game like you mgiht be thinking, though. It is still a shooting game and quick enough reflexes will get you through, so it's not like a shooting version of Rick Dangerous, with unfair deathtraps that are impossible to avoid on a first attempt.

Whipplu Special (X68000)

Just a small post to fill in a gap in my silly self-imposed "there has to be a gap of two posts between posts with the same tag" rule.
Whipplu Special (the name that's in the loading screen, if that's not what it says on the title screen) is a block-sorting puzzle game which, on first glance looks a lot like the SNES game Panel de Pon. It plays quite differently, though rather than having to form groups of touching blocks, the aim is to have three or more similar blocks on the same row, a which point they will disappear. Game over comes when you try to put a block into a column that's already touching the top of the field.  Also unlike Panel de Pon (an most other post-Puyo Puyo puzzle games, there's no kind of vs mode, nor does the game gradually get faster as you play.
The pace is actually a big departure from the genre at large, as the game is much more sedentary than it's peers. You can take as long as you want to eye up the situation before placing your blocks without penalty. Another unusual, but not unheard of feature is the way stages work in this game, being a system similar to some older versions of Tetris: each stage has a quota of blocks to be cleared, at which point it will end. Between the stages, you'll be shown a picture of some food, which is nice. There's also a Ranking Mode, the aim of which is to achieve as high a score as possible while removing 100 blocks.

Unfortunately, though the background art is a nice scene, it doesn't seem to ever change. Or at least, not as far as I've seen (having managed to get about 7 or 8 stages in). The music does change every few stages though, and it's pretty nice too.