There's a slight probability of something going wrong whenever you write to a card something will go wrong; the answer by @his covers this nicely, and in sum, it's not worth worrying about. There are, however, two reasons you might be legitimately hesitant.
First, the user interface on cameras is sometimes a bit clunky, and if you're in the habit of deleting files on the camera, it might be easy to accidentally delete a frame you want to keep. I've done this, and have since decided to avoid deleting in camera whenever possible — just swap memory cards when one is full, and sort them at home.
Second, if you delete files from the card, that leaves a logical hole in the data on the card, and future files may only partially fit in the hole, leading to file fragmentation, which isn't a big deal but will reduce your chances of recovering files if you need to run an undelete utility.
So overall, there's no real worry about corrupting the card, but avoiding deleting in-camera may reduce your risk of user error.