Well, electronics and software is part my profession, so I have some idea about this. With a computer system there are mainly two aspects to possible damage incurred by rebooting and power cycling.
One is damaging the content of persistent storage (usually magnetic discs or flash memory). That is why systems should be shut down according to their prescribed procedure. If you hit the power switch right in the middle of a write to persistent memory you may get corrupted files or entire file systems. However, if your system hangs after a crash, this point is kind of moot since it must be rebooted anyway. In the case of a gaming console, it's usually only writing to the hard disc when saving (or when downloading stuff, but then you usually don't play a game that will cause a hang). I.e. a game that crashes during gameplay will seldom cause damage to files and filesystems.
The other is inrush of current during power-on and thermal cycles as an effect of power cycling. These can have a cumulative effect. However for most consumer electronics this is nothing to worry about; the mentioned effects will not normally cause damage for the life time of the equipment. Also, thermal cycles will only occur if the system has time to cool down between power-off and power-on, which isn't the case for a quick reboot. For completeness sake, I'll mention that for systems such as PCs where you have a reset button, a reboot pressing the reset button will have none of these electrical or thermal effects.
Of course now and then a console dies, usually due to manufacturing defects, and unfortunately users are quick to hit the net with forum postings like "Game XYZ killed my PS3/Xbox/Wii", resulting in the creation of myths.
In conclusion, apart from ruining files, e.g. getting a corrupt game save, there isn't much to worry about.
DJ
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This will be my 4th
