Generic chargers, VZW's charger included, will indeed charge the phone without any problems. However, if you're using battery-intensive apps such as GPS, or running multiple semi-intensive apps at once, the VZW charger won't be able to keep up with the depletion of the battery. In other words, your battery will still drain even though it's plugged in. There's been a lot of talk about this on the forums and the concensus is that you're going to need a charger that pushes at least 1 ampere of electricity (1,000 mAh). The VZW charger pushes 750 mAh.
Just purchased this charger about a week ago. Works REALLY WELL!!! Also, can't beat the price. One note of caution, though - plugging the charger/phone into the auxiliary charger port, the battery may overheat and the charging will pause. Use the primary port (I used it with GPS on the trip from NY to PA, almost 3 hours, no overheating, battery stayed at 100%).