I elect two games for this thread
MDK: This third person shooter from 1997 basically introduced the variable scope sniper rifle to video games, but more than that it could shoot various types of ammunition, has three screens which display where bullets hit and can zoom in up to 100x! Along with some very varied landscapes contained on top of city-sized tanks, some great platforming level design and incredible subtle and in your face humour, this is one of my favourite ever games. My only issue with it is that it only had five levels and pretty much didn't have an ending. You kill the final boss, the camera swivels around it blowing up, then you return to the title screen. Not even any credits unless you select the option yourself. And MDK2... Was alright I guess. Just not nearly as funny or innovative as the first, although playing as three different characters with three rather unique playstyles was a very interesting addition.
And for my second nomination...
Future Cop: L.A.P.D. - At least if Wikipedia was to be believed, this was originally meant to be a sequel to the AMAZING Desert Strike and Jungle Strike games, where you flew around in a helicopter across an isometric level searching for objectives thanks to incredibly limited HUD. Then 'Future Strike' as it was going to be called got an overhaul and was made as a PS1 game about a mech running around/a hovercraft floating around levels shooting hundreds of badguys with three different types of ammunition which you could find unlocks for the further you progressed into the game.
While I didn't care so much for the campaign, one of the reasons I imagine it fell pretty flat since this was the era before a game could be held up by multiplayer content, thanks CoD, Halo, TF2, L4D etc. but this game had a surprisingly good multiplayer, based in five different maps of varied themes with only a single assault based gametype. Capture neutral turrets around the level to gain points, destroy enemy turrets to gain points, use points to generate offensive tanks and defensive helicopters, and the objective is to get one of your tanks into the enemy base. Sound simple? I DON'T THINK SO! as the game literally tells you in the training video for the multiplayer with a very over-enthusiastic voiceover.
Once again, I loved the humour in this game, with some incredibly silly visual gags which oddly seemed aimed at a younger audience despite the game featuring quite high levels of violence. Then again I was playing this game when I was seven so I found all the jokes incredibly funny. But gameplay wise it's still fun to boot up occasionally today.
It's a shame really, there was a remake of the game called Project: Resurrection which was intended to recreate the multiplayer portion of the game, along with extra game modes, level editor etc. but the site for it seems to have gone down, and has been down for quite a long time.
Also, Timesplitters, but everyone else has already said that.