Blood
Duke Nukem 3D
Shadow Warrior Classic
MDK
Doom/ Doom II
Rise of the Triad - Dark War
Blake Stone: Aliens of Gold/ Planet Strike!
Star Wars - Dark Forces
Crusader: No Remorse/No Regret
Slipstream 5000
Urban Chaos
Tyrian 2000
Sword of the Samurai

I'm not sure if all of these were meant to be played with just the keyboard, but that's how I always play them.
Some of them work best if you use the numeric keypad rather than the cursor keys.

The original (pre-AoD) Tomb Raider games. I don't know whether it's necessarily accurate to say that they were meant to be played with the keyboard, at least no more than they were meant to played with a console controller.

I think Blade of Darkness requires a mouse for the combat system, but I'm not entirely sure.

Tomb Raider 1-4 (and Chronicles) work surprisingly well with pure keyboard controls, but I'd recommend customizing them, the default layout isn't all that great.

In truth, I only wrote "meant to be played with keyboard", because I guess there are quite a few games that you *can* play restricting yourself to the keyboard but that are actually more comfortable to play with mouse (and keyboard), and I wanted those games that weren't made with mouse controls in mind at all.

Little Big Adventure 1 and 2. Both are fantastic games and are available on gog.

Almost all of the old side-scrollers: Dangerous Dave, Prehistorik, Secret Agent, Crystal Caves... I suppose lots of the new ones too, though some, like Pid, require a mouse.