Game technology is expensive. A not so known product like Unigine costs thousands of dollars, plus a similar amount per project. The number rises to hundreds of thousands when we talk about Unreal Engine. But, you don't need to spend so much to get into the industry. There are a few choices that can suit your needs of a full featured game or rendering engine.

Ogre 3D
Object Oriented Graphics Rendering Engine is the most popular free engine among medium to advanced developers. Ogre is a rendering engine, which means that it does not includes an input system, GUI, physics, sounds, etc. But when going to the graphic bussiness, it offers an impressive feature list. The lack of non-graphics related featyures can be solved with some of the many add-ons that integrate Ogre with other tools like Bullet or Newton.
This year has seen the arrival of more commercial products using this engine, like Venetia or the long awaited Torchlight. It is really easy to install under Windows, and not so hard under Linux if your distro has a decent repository. Although it is not so easy, two days are enough for any programmer with some experience to get used to the basic concepts.
Some people complains about the lack of an editing tool, but believe me, they are overestimated, I strongly recommend that you create your own level editing tool.

CrystalSpace
Even when they have the support of the Blender Foundation, who choose it as the engine for the Apricot Project, CS has always been like the second brother, shadowed by Ogre. They don't advance so fast, they have a much shorter list of projects (right now the most known is Apricot's Yo Frankie!, followed by Planeshift). Too bad, because CS is a full game engine: it includes supports for physics, GUI, scripting and all the elements involved in a game. They are not providing right now a precompiled SDK for Windows, that means you have to fight with the compiling hell. Under Linux I found a big problem: it wasn't ready for 64 bits systems, so I discarded it before further tests, but that has been solved in recent versions. Regrettably, this engine is not so easy to learn.

Irrlicht
Designed to be easy and fast, Irrlicht is like our toy car, eventually we grow up and get a real one (like Ogre). It is the recommended choice to start learning and it has a weird mix of features, like a GUI and its own XML parser. There are some extra tools like IrrKlang and IrrEdit, but they don't share the same license, and you don't even have access to the IrrEdit source code. But the community is strong and they have a few interesting projects.

NeoEngine
Once an interesting choice, it forked to a commercial version and a free one. The later seems to be pretty slow or abandoned.

Horde3D
This is an small rendering engine oriented to modern hardware (Shader Model 2 capable card or superior). Perhaps thye offer some good features, but other are severely lacking, like support for model formats other than Collada, or at least exporter tools for the major modelling tools.

Panda 3D

This is a game engine developed by Disney and maintained by Carnegie Mellon University's Entertainment Technology Center. They have some Disney projects in the list, but besides that, there is not too much buzz about it, even when it has some ointeresting features. You can develop in C++ or Python.

Soya 3D
This is an object oriented "high level" 3D engine for Python. Im not a Python user myself, so I have not too much to say. But besides Panda3D, this is the only engine for Python that you will find.

Apocalyx, Delta 3D
I dont have much to say about these engines. Apocalyx does not has a Linux port, so I discarded it. Delta3D is a game engine that looks interesting and it is based on free software, but I havent had time to test it.