Unfortunately external hard drives (3.5" HDD) require an additional power source. Internally they can take advantage of power from the PSU using molex connectors, but externally, USB and Firewire very simply cannot deliver enough power to the drive, hence a power adaptor.
Some external hard drive enclosures (though they tend to be cheap ones from china on eBay) come with, or are compatible with special PCI power brackets, whereby a molex power connector from the PSU plugs into the PCI power bracket on the inside of the PC. A power cord then plugs into the bracket at the back of the PC, while plugs into and powers the external drive. The drive automatically turns of after shutdown because it's powered by the PSU.
Your drive is powered independantly from the system's PSU. So, you're required to turn if off manually. I personally only turn my external drive on when I need it, and turn if off when I don't need it.
Because it's plugged externally using USB or Firewire, the drive is hotswappable, meaning you can unplug the drive and turn if off, even with your PC still on...well, as long as you don't unplug it or turn the drive off when you're still transferring data to / from it - this will damage files.
|Desktop PC| |Macbook Air 13" (Mid 2013)|
|Windows 8.1 Pro (x64)| |AMD FX 4100 Black Edition 3.6 GHz @ 4.0 GHz OC| |Arctic Cooling Freezer 13 PRO| |Gigabyte Nvidia GeForce GTX 560 Super Overclock 1GB| |ASUS M5A78L-M/USB3 Motherboard| |Samsung 840 Pro 256GB SSD SATA III HDD| |Kingston HyperX 8GB PC3-14900 DDR3-1866| |OCZ ModXStream Pro 700W Modular PSU| |NZXT Vulcan Micro ATX Case|