This is one topic that I wish I could have worked on this semester. I have plans on building a beast of a game though on my own, and possibly working on a distributed machine server system in HPC II.
I have learned a ton of information regarding 3d game design though, and if anybody is interested in learning more, I can direct you here where to find this information. These are links on what to learn and where to learn it using existing free tools and existing game engines. Writing your own from scratch would be a whole other topic.
The game engine is the base you build your game upon. It renders the graphics, handles the game scripting, and can either make you or break you. I've broken the list down to both free engines and pay engines.
Panda3d - Amazing engine, written entirely in python, and its free!! Disney uses a highly modified version for their MMO Pirates!
Ogre3d - I do not know too much about it but there are plenty of people out there using it. Graphics look a bit dated to me.
Irrlicht - Another open source engine, again the graphics look dated, but there's a community constantly working on it.
Hero Engine - Amazing looking engine! Just released an indie developer license, but its about $5000/yr + 25% of your profit.. Ouch! On the good side, you can sign up for a sandbox account and play away!
Torque Game Engine - Decent little engine - for $100 you can get an indie license, or download a trial of the tools for free.
Realm Crafter - Not bad in price, $165, but thats EACH seat, if you have two programmers, double it. The huge benefit here is that it has a mmo server built into it, and is specifically designed to create a complete game with it's tools. Scripting is in C#. Its in beta though, so be careful.
Blender - Blender is the best tool out there for 3d modeling, and to top it off its FREE - I will gladly stand the new beta of it up against the likes of 3d Studio Max - and the cost difference does it all.
Fragmotion - Funny name, but a great little program for animating your models.
L3DT - Another hard to remember name, but a great tool. Will generate MASSIVE terrains including their textures, from hills to mountains. Woo!