Can A Computer Run Without RAM?

Many computers run without RAM, but they're not the ones you normally would call a 'computer' for general purpose computation.  Computer chips are running everything now days, from microwave ovens to automobiles.  Some of these applications do very limited tasks and require only a few locations of memory, which can be handled by built into registers inside the computer CPU chip already.  The program to run these sort of devices is in ROM, which is a read only memory, that is programmed in the factory and never changes.

If you are talking about a PC the simple answer is NO