Mario 64
Rayman 2

It's all a series of tubes...
http://www.classicdosgames.com/game/Tube.html

It would have looked something like this:
http://www.mobygames.com/game/betrayal-in-antara

But that wasn't exactly state of the art when it came out. Better starting points are the Elder Scrolls up through Daggerfall and Battlespire, and Jedi Knight in software mode. Try Descent, too.

Oh, you might find Might and Magic 6 very useful, even though it's dated 1998.

Try selecting the years you want from this page. It should give you enough titles for reference.
http://www.mobygames.com/browse/games/action/dos/1st-person-perspective/

Is Castle Master early 3D or stone age 3D? http://www.youtube.com/watch?v=CyFK6xqjms4

Basically what I'm looking for is something that looks exactly like the screenshots I posted.

Exactly like the screenshots? This. Find videos of the top two games and try not to have nightmares. You might even play the games (they're absolutely free now).

Sprites on 3D retro Chantelise and the follow up Recettear in dungeon mode.

Of oldies Might & Magic 6,7 and 8 are a lot like this. So are Lands of Lore 2 and 3. Also Grandia and Xenogears and Dragon Warrior 7. Myth 1 and 2, Warhammer: Dark Omen and early Total War games used sprite units on a 3D terrain.

If it's very fun (I'm more of a Croc, Rayman 2, 3D action adventure games), count me in for support. :) I long to one day create an early 3D game too, probably because my best memories are from those days. Alas, given time constraints and my learning ability I probably won't know how to make them for a while to come.

How are you planning on creating it? Are you knowledgeable in programming, 3D modeling, etc.?

Disruptor hasn't been mentioned yet, that's well worth a look.

Hey man, I'm a modder so I can give you some links and recommendations on how to re-create some old style, colour bit pixel ranged 3D effects. Firstly:
http://www.telefragged.com/wally/
This program is what I use to create low colour bit textures and sprites that use a range of palettes. It's perfect when you want to build on an old engine or to gain that textured effect.

You can go ahead with building your own engine, but I would recommend, seeing as there is plenty of old engines out there which are now released Source code or adapted to be modified to modern day engines, but still show and can render old style effects is what I would recommend. This can be from the BUILD engine, the Doom engine or even the Quake 1/2 engine. Popular choices.

Best of luck! - Jazzbyte123

Oh, you were looking for Might & Magic 9!

Wolfenstein 3D - fun and puking for all the family!

King's Quest 8.

Terra Nova (1996)

Alone in the Dark (1992) deserves to be in this thread.