Can I upgrade my MacBook Pro using "generic" RAM?
Yes, you can buy third party RAM.  I usually buy Crucial RAM.  As long as it is made to be compatible with your machine (Same Bus Speed and such).  Usually, you can search these companies sites for RAM for your specific make and model MBP and they will have suggestions for it.  

You can sometimes even put in more RAM than Apple says it can.  The companies test newer machines to see how much RAM they can handle.  For instance, the new current gen MBP only supports 8GB according to Apple, but 16GB of RAM will still work and won't cause any problems. It will work perfectly. 

I am running 8GB of RAM in my machine, it cost me 46 dollars with shipping over 200 dollars from Apple.

Just be sure to keep you old RAM just in case your new RAM goes bad, which it most likely won't, but that way you have back up RAM to use in just such an occasion. 

I hope that helps.