Since hard drives have become a mature technology, the differences between them are more trivial. However, there are several models that are best for certain tasks. Depending on what the drive will be used for, rotation speed, reliability, storage capacity, and power consumption, may be important factors. But the most dramatic differences are between Hard Disk Drives and the newer Solid State Drives.
Traditional hard drives typically come in a few different rotation speeds including 5,400 RPM (most common in laptops), 7,200 RPM (most common for desktops), all the way up to 10,000 RPM, which has been reserved for high performance systems. If you're looking for a boot drive for a computer, a traditional spinning hard drive may not be the best option. Solid State Drives, while more expensive per gigabyte, is much faster and will have a huge impact on your computer's performance.
There are also hybrid drives that seek to combine the speed benefits of solid state with the storage benefits of spinning drives. However, hybrid drives generally don't perform as well as pure SSD, and Leo doesn't recommend them. Instead, it would be much more beneficial to have two separate drives -- a smaller SSD just for the operating system and applications, and another larger HDD for data.
Another thing to consider is the drive's reliability and longevity. One way to get an idea for how long the company expects a drive to last is to look at the warranty they offer for it. The top hard drive brands are Western Digital, Seagate, and Hitachi. Here at the TWiT Brickhouse, we use Western Digital drives and you can find a list of all the drives they offer here.
BackBlaze, an online backup company, uses over 25,000 drives and has done research on their drive failure rates. In their tests, Hitachi had the lowest failure rates, but they also tend to be more expensive. BackBlaze is currently buying 4TB Seagate and Western Digital drives. They've been avoiding the Western Digital 3TB 'Green' drives and the Seagate 2TB LP drives. Check out BackBlaze's complete report at blog.backblaze.com.