Thanks for the great replies everyone.
I am going to work through Seraph's tutorial as it appears to be exactly what I was looking for.
Most 2D games you see today are using either DirectX or OpenGL in some way to do their rendering.
How do you spot wether a game is purely 2D or just being 2D while using DX/OGL? I do not know much about the subject, but from what I can tell that bear fighting game I linked appears to be straight 2D without anything 3D-accelerated. Basically trying to see what the limits are to 2D as far as visual FX is concerned.
Also a few things about terminolgy.
DirectX and OpenGL are basically interfaces that allow the programmer to access the GFX card and SFML(and the others mentioned in the topic) are basically the same but without the 3d capabilites?