All 3.5" drives need 12V which USB cannot provide, 2.5" drives in external casings can either require one or two USB ports or come with a power adapter, usually 1-2 USB connections
However larger size can mean higher power draw. In the same series of drives (Barracuda 12 for example is 500GB per platter) 500GB is single platter, 750GB and 1000GB 2 platters, 1500GB 3 platters and so on, the more platters in a hard-drive the more power is consumed to spin the platters