Have an Elitegroup motherboard MCP61M-M3 rated at 1333 mhz. Want to buy fry's 4GB DDR3 1600MHz Corsair CMX4GX3M2A1600C9, will this run on my motherboard as it is only rated 1333 mhz top speed
If you are getting the 1600Mhz at very little price difference than the 1333Mhz version, then its okay to get it. Your ECS motherboard does not state support for 1600 so it means you have to take the risk that it may not be stable. If it is not stable, then you can just run your 1600Mhz RAM down to 1333MHz.
PS: Actually those RAM's that are sold as 1600Mhz are just 1333Mhz that has been guaranteed to run 1600MHz under OC. And in any case, I do not forsee that you will perceive much difference in performance running 1600Mhz from 1333Mhz.