Whatever you want to say about Doom 3 (and usually it's either "boooooooring" or "oh c'mon, it wasn't that bad"), it's fairly safe to say that it didn't really capture that classic Doom feel. That classic Doom feel being "aaaargh shoot everywhere all the time wheeeee boomboomboom", of course.
There're a few mods around that try to pull D3 back into the good ol' dark ages, but top-down singleplayer shooter Z-Hunter's an entertaining new kid on the block. A very stupid new kid for sure, but stupid often = fun.
Some sample lyrics from Z-Hunter's screamy-metal theme tune best sum up this mod's rethink of Doom 3:
"I don't need no ammunition,
I don't need no fucking health...
Fucking kill you,
Till you're dead"
There's quite a lot of swearing throughout the game, because swearing is big and clever. I think it's attempting to get across that this mod is dark'n'dirty'n'testosteronal compared to D3's relative sedateness, but really it's best to try and ignore the teenage text and puerile music and just enjoy the Alien Breed / Shadowgrounds top-down shootiness. There's nothing clever or novel to it - just waves and waves of zombies and hellbeasts, unlimited ammo and lots of explosions. Clearly there's a lot of distance between this and any actual Doom game, but it does capture the freneticism of the series' elders.
It also does a fine job of making Doom 3's Hell Knights and Pinky Demons terrifying again - the zombies and the like die incredibly easily, but when you've got a gigantic hell-thing galloping down the screen towards you, apparently blessed with infinite HP, and the clunky controls make turning and running away a near-impossibility, there's a glorious sense of panic and menace.
There's not much weaponry, the levels are very similar and the camera really is a pain in the arse sometimes, but it just about hangs together. You're better off with Shadowgrounds if you've a few quid to spare, but as freebie (if you own D3) this does the trick.
Go take a look, anyway. It's overwhelmingly childish, but in that "I just want to spend two hours shooting stuff into little bloody pieces" way we all crave from time to time.
Also, note to id: it really is way past time you patched official widescreen support into Doom 3.