How much ram is needed to run minecraft on a PC?

512 MB or 1 GB but the more the better

RAM has a little to do with it, but it's also processor power. The game is processor intensive. If you are playing single-player, you are being both the server and the client at the same time, which double-taxes the processor. So memory alone isn't going to tell you if you will have problems or not.

Total system RAM? At least 4GB. Give 1GB to Minecraft.

If you have 8GB total system RAM you can give 2-4GB to Minecraft.

Minecraft will take whatever RAM you can spare, and ask for more.

You need at least 512mb of ram to run it.

The minimum I have run minecraft on is a 1 GHz 2 core tablet PC with 2 GB RAM with AMD HD 6250 graphics. But that is just barely playable (faster in Linux than in Win7 Pro). Even with faster CPU, good luck with anything that has older Intel integrated graphics. It worked well with 1.66 GHz 2 core laptop with 2.5 GB and legacy ATI X1300 mobile graphics from 2005, but was unplayable on similar 1.66 GHz 2 core laptop with 2.5 GB and Intel graphics from 2006. Minecraft actually played about 25 fps on my Win8.1 4 GB work PC with more modern Intel HD graphics, but I did not try reducing graphics settings to see if it would go faster.

My home PC is a 5 year old i5 650 3.2 GHz 8 GB with Nvidia GTX 750 Ti and in fancy graphics settings in 64-bit Linux I have it throttled to 120 fps or it would go much faster most of the time (still over 60 fps chunk loading). It can run both a separate minecraft server and client, no problem.