These type of enclosed hard drives conform to the USB specification 2.0 specification, even though it's USB 3.0 it must be able to fall-back. USB 3.0 provides lots more power, but since it falls back it must conform to the USB 2.0 500 mA maximum current. The hard drive itself might use more power, but the built-in electronics will detect when to use staggered spin up (takes longer to spin up basically)
The inrush current must not exceed 500 mA either; this is when you plug it in, and it spins up. The 3.5" versions draw much more current on spin up since they always need a dedicated power supply and do not need to conform to the USB specification. That is why it's important to use at least a 1.5 A power supply. The Raspberry Pi can use 800 mA at peak times on its own. So if you have Wi-Fi maybe it's good to use 2 A or 3 A power supplies.
The Raspberry Pi was built to the USB 2.0 specification, but unfortunately due to hardware problems the Raspberry Pi resets itself (brown out) when it needs to provide the 500 mA inrush current because of poly fuse and voltage regulator problems or rubbish power supplies that cannot provide the peak current in time. The newest Revision 3, B+ or 2 do not have this problem and this USB hard disk drive will run without any problem.
To get it working on older Raspberry Pi's you either have to bridge the polyfuse or solder +5 directly to the +5 V USB pins.
I have used a few USB hard disk drives on older revisions using the workaround and it's stable.
The hard disk drive used in that enclosure is WDBUZG0010BBK.