How much Video RAM is needed to run Minecraft on medium settings?

Minecraft requires little ram but i doubt you would be able to have a lot of other applications running with it e.g google chrome and skype and steam try just minecraft and it should be fine also make sure your performance IS NOT on VSYNC it will explode your ram use max fps.

Probably very little, unlike most games it only uses a small number of simple textures, as well as not supporting antialiasing (well, not without the Optifine mod anyway). Large amounts of video memory are needed when processing lots of detailed textures and other effects like AA and anisotropic filtering.

With this game most of the work is done by the processor, and the heaviest workload is on the hard drive, which always seems to be busy.