External hard drives come in two flavours. 'Pocket' external hard drives are highly portable and lightweight, and draw power from the computer through USB for its functioning. They are ideal solutions if portability is the need. 'Desktop' external hard drives are larger in size, and require their own dedicated power supply. These are cheaper, have a stronger casing and usually come in larger capacities.
The factors to be kept in mind while buying an external hard drive for storing photos are:
1. Always go for a reputed brand. It doesn't make sense to try and save a few dollars when it comes to risking all our memories gathered over so many years. Though there's no guarantee an external hard drive manufactured from a well known brand won't break, the chances of it happening is definitely smaller.
2. Go for as high a storage capacity as you can afford. Plus a little more. With cameras producing increasingly larger sized image files and digital technology making us shoot more photos and videos than ever before, it'll never hurt to have extra storage space at your disposal.
3. Choose high speed connectivity (for example, FireWire 400 or 800) over USB 2.0 if you're a regular photographer. Though costly, the speed difference it offers is considerable.
That said, let me quickly run you through some really good external hard drives. This list is not exhaustive, and there are many other reputed brands available. It's just that you won't go wrong with these!