I'll just recompose most of the answers and add some new ones:

Duke Nukem 3D
Blood
Rise of the Triad
Blake Stone series
Realms of the Haunting (warning: has plot!)

The above games can be bought on GOG.com.
The list below, well you'll have to dig hard for those.

Outlaws
Shadow Warrior
Witcheaven
Witcheaven 2
Chasm: The Rift
Powerslave

You're most likely aware of it, but there's a huge amount of high quality mods and levels out there for the games you've mentioned.

Why not try out something like Alien Vendetta?

There enough levels and conversions for Doom to prevent you from resorting to surrogates like Serious Sam for years.

Playstation version.

Actually if you can get PS1 (or an emulator) running you might find a few interesting things.
http://www.youtube.com/watch?v=YWKgY7zKFgo
http://www.youtube.com/watch?v=--GQT1ibZFk

Get free Zero Tolerance for Sega Genesis, too.

Painkiller - http://www.youtube.com/watch?v=YiS1p45Z9NA

A great game. If you loved the Doom series.

There's a mod for Doom called "Doom Aliens", i can remember it's really cool, you should try looking for it.

I'm gonna throw Tribes Ascend out there. It has no plot really, is all arena battling (on large maps), and is very old-school in that it's a very quick shooter. Just be sure to go through the tutorial first since the game implements some unique gameplay mechanics to make it even faster.

are you talking about 2.5D?

Only one I can think of is 8-bit shooter, but it seems to have been pulled from all corners of the internet. Pity.

It's 8-bit killer. http://www.locomalito.com/8bit_killer.php

Thanks!

It varies on what you want to do with your mod. Some people just release map packs, some people change all the maps, graphics and sounds but require people to provide the original EXE to play, or you can go all-out and start editing the source code as well.

Orb changed everything in the game and took me awhile to do. There's an active forum of fans and modders called DieHard Wolfers where you can find information, tutorials, etc. Editing the maps, graphics, and sounds requires an editor such as WDC (one I wrote) or ChaosEdit. The source code uses Borland C 3.

There is also a Wolf4SDL port that allows you to run the game in Windows. This was released after Orb and I've not yet got around to changing Orb over to it.

Ah, I see. Thank you.