The adapters you're speaking of are generally just a transformer, a rectifier, and possibly a regulator to convert your AC power from the wall into +5V DC, and the output is connected to the power pins on a female USB plug. If anything, it's safer for your USB device than a computer USB port, as there's likely to be less voltage fluctuation and there should be ample current.
Most computers have a 10% "tolerance" on their 5V line, meaning it could be outputting anywhere from 4.5V-5.5V (and some exceed this tolerance, especially if the power supply is being pushed to its limits). Even with these fluctuations your device will be perfectly fine since they're designed to deal with this sort of output - but when using a dedicated power supply (such as an adapter), you're almost guaranteed to get 5.0V, and there will be more than enough current to allow it to charge.
Hope this helps!
Right first of all I don't yet own an mp3 but am looking around at the moment to buy one.
One that's tempting me so far is the sony nwe-005
It has good battery life and charges dead quick when usb plugged in to the pc
Now i'm not always going to be near a pc when the thing runs out - ie a 2week holiday abroad with no pc access.
I've seen USB chargers though that plug in to the mains socket and then you just plug your player in to that.
Are these ok for all players or would this not be recommended? Would I therefore be better with a speaker dock even though I'd never use the speakers?