Open-source engines have excellent technical quality. Just think about it, a mistake on these engines would have to go through tens of contributors in order to make it in. Usually, the problem with open-source is finding one that suits you as well as Source Engine, or other commercial ones. Still, if you don't need uber-fast up to 50 player networking, advanced AI scripting, why bother? An open-source can give you the same result on the stuff you really need. Just have to pick the right one.
That is what I was trying to say. I didn't thought on building a game engine, at least not a multipurpose, reusable tool that everyone of them tries to be.
I just want to build a game without a game engine.
I see we are getting you even more confused here.
A game engine is a system designed and developed for creating games.
You can use a multimedia library like SDL, a physics engine like Box2D and ultimately a data storing, let's say sqlite, and on top of that build your own game engine. That does not mean your game's engine has to be reusable or it is not an engine, it may not be a super-reusable software framework or something fancy like that, but it'll be your game engine. Also, I would say you used 2 game engines, SDL and Box2D, to build your game's game engine.
Just that SDL addresses multimedia, input, networking [...] while Box2D addresses the physics, collisions, simulation [...] and your own game engine, using the other two, addresses everything from input to physics to loading levels.
Ideally, the time you spend writing your game's engine has to be minimal. This way, you can focus on adding content and quality to your game.
Unless you have technical requirements that force you to spend more time on the engine (see airplanes/trucks/trains simulators).
And as Dwarf King posted, Ogre3D is really good, I used it and confirm it. Still, if you want to look them up and choose one that fits you, go ahead: