Getting smooth, big points in OpenGL

Question

I started playing around with OpenGL and GLUT. I would like to draw some points, but the problem is that they turn out to be squares, and I would like them to be round dots

Answer 1

Mads' answer provides everything you need if you go for the fixed function pipeline. However, if you have a system that does not provide the ARB_point_sprite extension or with a broken implementation (some ATI drivers), you can solve this part also with geometry shaders. The ARB_geometry_shader4 extension allows you to convert a point primitive to two triangles, which can be used as the quad created by the ARB_point_sprite extension. On OpenGL 3.2, geometry shaders are already supported in core, no extension needed. The OpenGL wiki has two examples.