When it comes to packing more storage into Mac systems, the only model that Apple supports adding more internal hard drives to is the Mac Pro, where you have four drive bays to use for new hard drives. While drives on other Mac systems may be user serviceable, the only supported options for adding more drives to them is to use external storage options.
External storage options are relatively fast and easy to set up, however, they do offer a bit of an inconvenience as they can clutter your workspace, or be a burden to lug around with a portable system. In addition, most are not as fast as internal drives and better serve as a storage option for larger and less-used files rather than as a medium from which to load the operating system and applications for day-to-day use.
Luckily, even though most Mac systems besides the Mac Pro come with only one internal hard drive, there are options for putting more in these systems and expanding your storage capability using faster SATA connections and not having to worry about clutter.
In systems that contain optical drives, you can replace this drive with a high-capacity hard drive or high-speed SSD by placing a bracket in the drive bay that can be purchased from companies like Other World Computing or OptiBay (Iin one of my Macs). Similar brackets are also available for the optical drives in iMac and Mac Mini systems.
While for iMac systems you can replace the optical drive and use its SATA connection for another hard drive, in newer models Apple has included support for two SATA devices on the optical drive's connection, allowing customers to select dual drive options on supported systems. However, if you have purchased an iMac and only chose a single hard drive configuration, or purchased the 21.5-inch system that does not come with drive customization options, then Apple does not include any bracket or connection to attach a second drive, even though such a connection would work.
To tackle this and allow you to install a second hard drive at a later point, Mac repair site iFixIt has come out with a small $69.96 adapter and installation kit (one for the 21.5-inch iMac, and one for the 27-inch iMac) that will allow you to put a second drive in your iMac. Unlike other kits that might replace the optical drive, this one will result in the new drive being right behind the optical drive and thereby allow you continue using it.
The kit comes with an SATA data cable and a custom SATA power cable, along with all the tools necessary to open the system and manage the delicate connectors and components in it. Using this kit you should be able to put any 2.5-inch SATA drive in your system and either increase speed with an SSD as your boot drive, or add more storage. If you do not wish to spend much on a large SSD, you can get similar performance by using a smaller SSD (up to 128GB) as a boot drive and then storing your larger files and data (such as iTunes libraries or movie collections) on the slower conventional hard drive.
Do keep in mind that while these bracket and adapter options are available, they are not for the technically timid. Installing them does require a fair amount of disassembly and manipulation of delicate wires and connectors that could easily be broken if you are not careful. While iFixIt does offer a very detailed and clear step-by-step guide for installing its drive mount, even with this option some people may be uncomfortable with performing these modifications.
Even if you do feel comfortable with it, I recommend you only attempt this if your system is out of warranty and if you would find it far more beneficial to have a second internal drive than resort to using external options.