If you are using OpenGL, the OpenGL FAQ section 9: Transformations covers exactly how to do this. And no, it doesn't involve raytracing, as that's understandably a very inefficient (but high quality) way to accomplish this.
9.170 How do I render a mirror?
Here is essentially what the FAQ entry says, and the example code demonstrates:
- Set up a reflected view matrix. Doing this for axis-aligned mirrors is explained in the second paragraph.
- Draw the scene
- Restore the view matrix and clear the depth buffer
- Render the scene again; the actual mirror geometry in this scene should be translucent or entirely transparent, in order to show through to the previously rendered mirrored scene.
Obviously there is a lot of room for optimization. When rendering the reflected scene, you should probably as much culling as possible, since mirrors are typically small and the default off-screen culling won't kick in for the geometry which is on screen but not seen through the mirror. You can also render just a simplified version of the scene through the mirror. For effects, and to obscure the user from noticing the reduced quality, you could apply a shader (e.g. blur, or maybe bright/washed-out) when you do your mirrored render.
I imagine, if you're using DirectX, the procedure would be much the same.