There are a few types of cable that you will need inside your computer. IDE cables are for connecting hard drives and CD/DVD/burners. Floppy cables are for what they sound like, connecting floppy drives (or older tape drives). Floppy and IDE cables cannot be linked together. Also, the bundle of wires that come out of your PSU counts as cabling in your box.
There is a limit of two drives per cable (occasionally you will run across an IDE cable that only has a connector for one drive) and most motherboard come with at least one cable of each type as _slh_ has observed. Also, if you look around, you will probably find someone who still makes a two drive floppy cable. Usually you get the flat ribbon cables for free but most of us use round cables in our computers these days to improve airflow.
There is also another cable called SCSI (pronounced Scuzzy) that are used in situations where two drives are not enough or higher transfer speeds are required. SCSI cables also come in both flat and round varieties. SCSI devices can be linked together for a maximum of either eight or sixteen drives. However, SCSI drives are a good deal more expensive than IDE drives so unless you are building a server you should go with the IDE drives to keep your costs down.
Serial ATA or SATA is the new kid on the block as far as drive interfaces are concerned. To my direct knowledge, there are no round SATA cables but they are small enough that there is probably not much point to rounding then anyway.
In addition, you may use various other cables in your box. There is a thin cable that connects your CD drive to your sound card. It makes an analog connection for playing audio CDs. If you have to add external connectors such as extra USB ports or the breakout box included with high end sound cards, you will have cables for those as well. If you use a fan controller, you will also have still more wires crossing your box.
