Is there any algorithm for converting 2D video into 3D video?

No - 3D video require that extra information (depth) be present that simply isn't contained in 2D video.

If you have a 2D rendering of a sceene (for example in Toy Story) then its quite easy to produce a 3D film - you just change the viewing angle of the sceene and re-render.

Well, Stanford does have an algorithm for converting 2D photos into 3D models. My guess is that with movies it should be even easier, because then you have several photos instead of just one, so you can extract much more information about depth by comparing neighboring frames.

Arguably, the results will never be quite as good as when you just render/shoot the movie in 3D to begin with.

It cannot work in general for a very simple reason: Suppose you have a scene with a window in a wall showing a beach, and beside that, you have a photograph showing a window in a wall showing a beach. How can the algorithm differentiate between the two? How can you detect what is reality with depth and what is just a flat photograph?