Specifically, some enclosures can have limits relating to the SATA/IDE controller built into the enclosure.
All 2.5 inch HDDs I've seen have roughly the same power consumption (depending on 5200 or 7200 RPM mainly). Every single one I could operate with the 2 USB cables included with the external hard drive cases. If I plug it into the back of the PC I often only needed one USB cable. Using plugs on USB hubs will often cause problems, though.
USB sockets, per specification, can output up to 500 mA.
Practically 2.5" hdds could use from 600 to 1100 mA for running up. The high power consumption for this short time is - most of the time - allowed by motherboards. When running they will need about 250 to 400 mA, so they are way into the USB specification there.
3,5" hdds will NEVER work from USB alone, since they need +12V power and for a conversion there just aren't enough ampers!