CARRiON-XCII: I think most RAM heatsinks are just for show, so if you do it cautiously there shouldn't be a problem. But don't quote me on that as I've never done it myself. I usually get RAM that doesn't have big fancy heatsinks. One wrong move and it's probably RIP RAM stick.
Removing the heatsinks would likely void the warranty on the RAM. IMHO, they wouldn't put them on if they weren't necessary, it's just not that important for the RAM to look cool.
ignisferroque: I've 2 triple sets of Ram installed, both by Samsung but one set has heat sinks. The difference in temp is pretty low, around 3-4°C. So technically it shouldn't be a problem to remove them.
That said, RAM can get a bit warmer when doing heavier tasks, I would't recommend stuffing a hard disk directly next to it
That's the other part of it. If you have to remove the heatsinks in order to cram other things next to the RAM, especially if those things generate heat, you really ought to be thinking about other possible ways of handling things.
Removing the heatsinks if the RAM is completely isolated with plenty of room for air to pass by is one thing, or if it's in the path of a fan, but removing them when you're constricting the airflow and adding another heat source seems to beg for system instability issues.
Granted there are numerous variations here that can affect the end result, but I'd be hesitant when removing things like that.