I'm biased because it was the first FPS I ever took online, but man did I love Shogo. The multiplayer was deathmatch only, but I've never played a deathmatch quite like it.
It was insanely fast and manuverable, both on foot and in mech, but instead of Quake or Unreal style bunny hopping, where you have to keep hopping in one general direction to keep your speed up, there was a top speed you hit almost instantly, making crazy dodging possible, where you and your opponents were rapidly jumping, crouching, changing speed and direction[footnote]especially in the mechs, which had a vehicle mode that made you faster, lower to the ground, but slightly harder to change directions, that could be switched in and out of instantly with a button press[/footnote]. On servers that allowed it, there was also the tractor beam, which allowed you to basically fly slowly in a straight line (which made you an easy target and added another layer of strategy), and get to really crazy positions -- it was an FPS that you actually needed to worry not just about opponents around you, but also above and below you.
The tractor beam could actually connect to the skybox, which made things even crazier. On some of the bigger maps, two players might wind up shooting at each other and dodging for a solid two minutes before either of them actually went down, and more often than not there'd be other players in there that would try to pick off both of the two who were dueling, that they'd have to deal with. It's the single FPS I've played that was the most skill based. A new player stood no chance of getting a single kill against even a moderately skilled player. The best players were untouchable dodgers and impeccable aimers, who knew how to use all of the weapons to the greatest effect. It also had one of the best shotguns ever. Heck, pretty much all of the weapons were great, especially once you get past the pistols/pulse rifle on the list.
The single player was cool too, although I'll admit I cheated to finish the story. But then I was 12 and didn't realize that there was a point in using anything but the keyboard with an FPS until after I started taking Shogo online. And yeah, I did it specifically to finish the story. This game did so much of what Half Life did, but came out just a couple of months before it, and people ignored it in favor of the much more heavily hyped Half Life. The biggest thing it lacked was the whole "stuck in one facility and one camera location for most of the game" thing, trading those for locations that change in ways that make sense for the story while still being realistic[footnote]for example, the first few levels have you shooting up an enemy base, going back to your mother ship for some information on the situation, taking a train inside that massive ship to get to where your commander is waiting to give you your orders, and then going back to the surface of the planet, where the story /really/ starts[/footnote] and cutscenes that admitted they were cutscenes, and worked better as a result. Not that it totally lacked story events that played out without breaking first person, it's just if there was a scene where the main character was talking to someone, the camera pulled back, let you see both people, and your character actually talked, instead of being a mute that nobody acknowledged was a mute. If I could switch places with a me from a universe where Monolith came out on top there instead of Valve (especially if it was one where Epic kept the niche it carved out with Unreal, which came out around the same time as the other two), I'd probably do it.