Running any electronic device does put some strain on it, and leaving it plugged in constantly is worse for it than unplugging it, plus you don't waste as much electricity if you unplug it when you aren't using it. Even if you do leave it plugged in constantly though, I don't think it's a device you're likely to wear out for quite a few years.
One thing I'd be a little concerned about though is the lights...some of my older devices that have lit displays on them have faded after being left on for many, many hours. Hopefully newer lights will last longer since they have better technology behind them, but all lights do eventually fade and fail.
Overall though, you're unlikely to wear out this type of device in the time you're likely to have it just by leaving it on. I'd still unplug it when you remember to save electricity though.
Where'd you find someone willing to part with one anyway? Do they have another!?