Phone connected to charger full time - never sleepmode - any danger? Yeah, might sound strange, but I managed do install Debian Linux on my Android phone. Because the phone needs very little power, it is, for me, the perfect server.

I plan to disable sleepmode and to leave the charger connected to the phone at all times.

Is there any danger in overheating, fire and so on?
Depending on the phone, my biggest worry would be screen burn. I have a Samsung Galaxy S Vibrant and I have screen burn at the top of my screen from the time and the notification bar.  A screen like a Super AMOLED is actually a lot easier to get screen burn then I thought it would be. It is actually pretty annoying now, I have to limit the background images I use, otherwise the burn is really noticeable.