Everblue (PS2)

Although i'd never heard of this game before a few days ago, it was apparently popular enough to get a sequel, as well as two spiritual sequels in the Endless Ocean series for Wii (which I also haven't heard of, though I admit the Wii is one of my blind spots).
Anyway, the game's abut diving and looking for treasure on the ocean floor. There's also some plot regarding an ancient civilisation or something, but it doesn't come into things until much later in the game. Other than that, the game's setting is mostly pretty realistic, with only very minor fantasy elements.
For most of the early game, you'll be walking the ocean floor, tapping your sonar button until you get a hit on some treasure, then closing in and taking that treasure. Then you take it back to the surface to evaluate and sell it or give it away to someone who needs/wants it. you should also be careful, as you can sell items needed to complete optional side quests, and even progress in the story. So only sell items that you have more than one of. Eventually you'll start finding shipwrecks, which you explore with full 3D movement, and you'll look for treasure inside those too.
The second shipwreck, the Juno is harder to fin than the first, since you won't be given directions until you beat a guy in an underwater swimming race. This race is the worst part of the game. It's too hard, boring, doesn't fit in with the feel of the rest of the game, and comes accompanied with some awful background music. Luckily, the ship is actually there whether you get the directions or not, and you might even be able to find a handy map on some cool internet blog if you look hard enough.
Although the game itself is actually quite repetitive, it never becomes boring. Finding a bunch of mysterious items and finding out what they all are is pretty cool, and the game has a great atmosphere too. Inbetween dives all your quests, shopping and item appraisals take place in the two small towns on the island. These bits add a lot to the feel of the game: they're always sunny, the people are all friendly, and the whole experience just feels really warm and happy. Interestingly, references to things like romance, alcohol, death and so on, that often get removed in English translations of videogames are left intact here. (And by death, I mean in the sense of an old woman missing her late husband, and so on, rather than the usual kind of videogame deaths that only serve as catalysts for more conflict.)
Another noteworthy aspect of the game is the complete lack of conflict. Even the guy who challenes you to a race does so only out of friendly, time-killing rivalry. There's no enemies or hostile creatures underwater, no evil regime to overthrow on land. It's actually quite refreshing to play a game that's so completely positive!
I thouroughly recommend you play this game if you have the chance.

Kyuutenkai Fantastic Pinball (Saturn)

So, Technosoft (sometimes known as Tecnosoft, for some reason) have made a lot of excellent games, usually with excellent music. One of their better-known titles is the Mega Drive port of Devil Crush, also known as Dragon's Fury. Like Kyuutenkai, it's a pinball game, and a lot of elements from Devil Crush made their way into this game: a main table being three screens high, bonus stage/boss fight sub-tables that offer huge amounts of points upon completion, even some smaller details, like the bonus counter with its two stacking multipliers.

Being on the Saturn, Kyuutenkai has some stiff competition from Kaze's Digital Pinball games, Last Gladiators and Necronomicon, and by "stiff competition", I mean "the best pinball videogames ever". Obviously, it's not as great as those two titans of the genre, but it does at least serve as a worthy follow-up to Devil Crush.
The main (and only) table is, as I said, three screens high. Each screen has a set of flippers at the bottom of it, and the whole table has a nice theme to it, with heaven at the top, earth in the middle, and hell at the bottom. There's lots of things to hit, and gimmicks to activate on the main table, like the angel watching over the middle portion of the table who can be made to shoot laser eyes all over the place, and the little band of skeletal day of the dead mariachis who can be knocked down in hell.
Obviously, the cute fantasy visual style of this game is massively different to the heavy metal album cover-inspired look of Devil Crush, and the bonus stages follow suit: instead of smashing open coffins or fighting multi-headed dragons, the bonus stages are cuter and more imaginitive to boot. My two favourites of the few I've seen are one that takes place on a football pitch where the player has to score 4 goals past the devil goalkeepers and his mummy defenders, and another where you have to use the ball to smash up the contents of a girl's bedroom in a strict time limit.
Although Kyuutenkai isn't as good as the mighty Digital Pinball series nor does it have the excellent music you would expect from Technosoft
, it is still a lot of fun to play, as well as very fast paced and even more addictive. There's also a Playstation version which I haven't played, but I assume it's' pretty much the same as this one.

Motor Raid (Arcade)

Before I start, I should mention something: the actual arcade version of this game comes in a full-sized motorbike cabinet that the player sits on while playing, tilting left and right to steer. I didn't play like that, though. I played Motor Raid via the excellent Model 2 Emulator, using an Xbox 360 controller.
With that out of the way, I'll get on to actually talking about the game. It's a lot like the Road Rash games, but in space and with luxurious and beautiful Model 2 3D graphics. You take part in motorbike races across various planets, and you have the option of attacking your opponents, punching them, kicking them, or clobbering them about the head with your weapon.
There's also a boost meter that gradually fills up as you race. Once it's more than half full, you can double-tap (or on the real arcade machine, I guess you would double twist?) the accelerator to use it. Obviously, the more you let it fill, the longer your boost will last. Less obviously, if you wait for the meter to fill completely before using it, you'll become enshrouded in an energy field and spin your weapon around your head.
There are four main planets upon which the races take place, though you'll only actually race on three of them in a regular game. Your performance in the races decides which planets you visit. I've read online that there's also a fifth planet which appears as an extra fourth race if you manage to place first in all three regular races. Unfortunately, I'm not good enough to make this happen, so I don't know what that extra stage is like.
There's a few characters to pick from, but since I'm not good enough at racing games to really tell the difference, I just pick the default character everytime, a young woman named Robin. After each race, Robin recites the cryptic quote "I won! But I still can't find what I'm looking for...". This is never explained.
In conclusion, Motor Raid is a really great game that you should definitely play, if you have a computer good enough for Model 2 emulation (pretty likely), or you live near a place that has an actual machine (not so likely). It's a shame it never got a home port, but I assume that's because the Saturn had no chance of replicating this game's graphics, and by the time the Dreamcast came along, Model 2 games were starting to be considered "old hat".