If you're not planning to add more than one expansion card (say, a TV tuner card) to your system, a mini-ITX board in a low profile or home theater case fits your needs. If you want two to four cards (tuner card, dedicated graphics card, dedicated network card, etc), a microATX board in a low profile case will work.
Note that a low-profile case uses narrow "low-profile" expansion cards with a special bracket; normal expansion cards won't fit. Most home theater cases have a right-angle riser that lets you use a standard expansion card. In both situations, you may need a power supply sized for the case rather than a standard ATX power supply.
Many smaller cases have bays for laptop (2.5") hard drives and slimline laptop optical drives instead of desktop-sized drives, so make sure you check this when selecting your parts.
In theory, you could fit a full-sized ATX board in the available space, but the logistics of placing the power supply, cooling system, expansion cards, etc. means you probably won't be able to find a case that can do the job.