If you ride your bike as a hobby on the weekends, you may not need a lot of storage space. It's not like you're hauling groceries or packing for a long trip. However, if you're riding across several states or use your bike as your primary form of transportation, you may need some space to haul things. There are several different options, and the right one for you depends on how much you expect to carry.
Most motorcycles have room for a saddlebag on either side. Also called panniers, saddlebags usually come in pairs. You attach one to each side of the bike behind and underneath the passenger seat. They come in two types: there are soft panniers made out of leather and other pliable cloth and hard panniers made out of plastic. Almost all saddlebags can be locked to the bike and have lockable closures so they can't be stolen. Some are even designed to function as bags when removed for their mountings.
Small motorcycle trunks are also available. These storage compartments are mounted behind the seat and do stick up a bit. They sometimes make a backrest for the passenger seat. Like panniers, they are locked in place and have locking lids. They can be used in addition to panniers for long road trips.
If you have a trailer hitch on the back of your motorcycle, you can purchase a small trailer to pull behind it. These trailers have two wheels and provide a good amount of space despite their small size. They're useful for long trips or for carrying larger loads.
Finally, you can add a sidecar to your motorcycle and use it for storage. While it doesn't features as much room as a trailer, it does make it easy to throw items like a briefcase or backpack into the seat and then quickly pull it out when you arrive.
