Nope, I'm running mismatched RAM and have been for years. The type (DDR3, DDR2 etc) has to match, and they have to be capable of running at the same speed, voltage and timings. (1333mhz, 1.65V and 9-9-9-24). It just easier to buy the same brand/model but you don't have to.
Everyone should build a computer instead of buying a pre-built one, or buy a Mac IMO.