How much storage do you need? In general, the bigger the capacity, the less you'll pay per gigabyte, so it makes sense to get the biggest drive you're likely to need. The highest capacity external hard drives for desktop use can have up to 8 TB of storage, whereas portable models rarely offer more than 4 TB. Those who intend to back up a lot of multimedia files like photos and videos should consider a drive with at least 1 TB.
How will you use the drive? If you'll need to take data on the go, consider a portable drive that's small enough to carry with you and doesn't require an external power supply. While these generally hold less data than desktop drives (typically maxing out at 4 TB), most still offer enough capacity for most personal storage needs. Also, portable drives pull power solely from the USB port, so they can drain a computer's battery faster than a desktop drive. An external solid state drive (SSD) will be more likely to survive a drop, and slower to fail in general than a regular spinning external hard drive, but it'll cost more.
How will you hook it up? An external hard drive is useless if there's no way to connect it to your computer. Most drives can handle a USB 3.0 connection, and some newer drives can use Thunderbolt or Thunderbolt 2 -- the gold standard for speed. If you have an older computer, with support only for USB 2.0, an external hard drive will still work fine, but data will transfer more slowly. A few drives offer wireless connectivity, which can be especially handy for use with a tablet or smartphone, but is typically slower.
What kind of computer do you have? Some external hard drives come with preloaded software that can make backing up files easier. However, in many cases, the supplied software is for Windows only. Mac users need to make sure that the drives they buy are either formatted specifically for a Mac or can work with Mac-compatible third-party software, such as Apple's Time Machine.