Hiya.
Ok, if you don’t mind spending a little bit of money…you can take a look at these:
$100 = Torque: http://www.garagegames.com/products/1 (full source included)
$100 = C4 Engine: http://www.terathon.com/c4engine/index.html (full source included)
$100 = Cipher: http://www.cipherengine.com/ (full source included…I believe)
$500 ?? = Nebula Device: http://www.radonlabs.de/nebula.html (not sure about how this works, but the base engine is free…kinda confusing; asked to contact them about source code)
Those are the ones that come to mind as “cheap” but you still get source code. There is another called “Sylphis” ( http://devnet.sylphis3d.com/ ), but they seem kinda chaotic about how and when they update and stuff.
Personally, I am using 3D Game Studio ( http://www.conitec.net/a4info.htm ) for one project, and we are probably going to use either it or C4 for the next. With 3DGS you don’t get full source code, but the SDK is fairly open…and the company rocks on toast!
Those guys at Conitec really are helpful. They will even actually listen to their customers and create specific ‘things’ into the engine’s next release just for you. How cool is that? The next release, “A7”, is going to have Octree as well as BSP, so wide-open game worlds will be easier to implement.
Anyway, good luck on whatever it is you’re doing! 