The only thing that matters is how much power the drive consumes. In general, large 3.5" hard drives draw more power then what even two USB ports can provide, whereas smaller 2.5" hard drives can be powered from one or two USB ports.
For reference, a single USB port can provide a maximum 500 mA of current. A 500GB Western Digital Caviar Blue 3.5" hard drive, on the other hand, requires 1220 mA at idle, and 1360 mA when reading/writing files to/from the drive. The 2.5" version of the drive (500GB WD Scorpio Blue) requires significantly less power, drawing 400mA at idle and 500 mA when reading/writing.
It is part of the USB specification that if a device attempts to draw too much power, it is simply disconnected from the target system. This is why some enclosures require you to plug in two USB cables. However, to get a full 3.5" HDD working, you'd need the power of almost four USB ports to get the HDD working, which is also why you never see full 3.5" drive enclosures without an external power supply.