there are lots of OpenGL tutorials out there - I think more than 90% of them make use of glBegin()/glEnd() with vertices set between these two calls. Now I found some people telling me these functions are deprecated and no longer available in newer versions of OpenGL.
So: is this correct?
In my application I have to be compatible with OpenGL 2.1.
Yes, glBegin()/glEnd() methods are deprecated. glDrawArrays is a modern approach and it is available in OpenGL 2.1. Here is related question on SO.
Also, I doubt about this 90% value.