Michael is on the right track. Some external hard drives lacking their own power supply simply cannot get enough power from a single USB port. It is most noticeable in the "name brand" drive that the office supply and computer superstores put on sale every other week. Their chipsets seem to be better optimized for Windows than Macs.
Flash drives work because the don't have a power-hugry motor that must turn.
There are two easy and inexpensive cures that allow you to keep your current drive:
If you need the computer and drive to work together in an environment lacking a power source for the hub, and the y-cable isn't an option because you have too few available USB ports, then your only option is to replace the current drive with one better optimized for Macs, like these:
http://eshop.macsales.com/shop/firewire/on-the-go
This particular one has the option of running on power from the computer's USB ports or, with an optional power supply, wall power. A good compromise for both remote and desktop use.