I used a product called Power Bridge (
http://www.powerbridgesolution.com/ )
It's similar in concept to the product from Panamax that is mentioned above. You can buy stuff direct from Power Bridge's web site, but various other places sell the same product. For that matter, I think Best Buy carries it, albeit at higher prices than online.
You basically have a reverse (male) power connector at the plate that is low down on the wall. Then you use normal Romex for the in-wall wiring between the two plates. At the plate behind the TV is a regular outlet. Power is brought to the lower plate by a normal extension cord (they provide a short one in the kit, since normally it will be either run directly to a nearby existing outlet, or possibly to a power-strip for lightning protection).
Because the wiring of the Power Bridge never involves live circuits, it gets around some of the legal restrictions on doing electrical wiring without permits or inspections. And I suppose it is somewhat safer during the installation process. If you live in an area that doesn't allow the use of normal in-wall Romex, you can use metal-sheath wiring.
The version that I bought has a second open cutout to pass other cables (as in the web link) - I have 3 HDMI cables routed to my TV (2 in use at the moment). Standard dimension "Decora" style wall-plate inserts (the ones that fit into basically a rectangle opening within the actual wall plate) can also be used at the "other wiring" cutout - I used an insert that has three HDMI connectors, for the end that is behind the TV. You don't have to buy the inserts from Power Bridge - any "Decora" format insert will fit. Home Depot carries a fair assortment, although they only had single and dual HDMI inserts, not the triple I was looking for. (So in summary I ran short HDMI cables from the TV to the wall plate insert behind it, and then have longer HDMI cables running through the wall to the lower plate. At the lower end, I have about 3 feet of the HDMI cables just coming out of the wall, to avoid a second set of connectors, but I could push those cable ends inside the wall and use a second 3xHDMI wall plate connector insert, if I wanted a slightly neater appearance.)
The length of Romex that comes with the Power Bridge kit is enough to go between a wall mount and a lower plate that is directly underneath. In my case I needed a longer length, as I was also moving laterally past two studs. If you are just dropping down vertically the installation is very simple - bypassing studs requires a bit more work, and or creativity....
One other tip is that in fishing the HDMI cables through the wall, I found it was better and easier to avoid higher-priced HDMI cables that are thicker. I needed 10-foot cables, and found some inexpensive high-speed cables at either Monoprice or Ram Electronics (online). I bought one supposedly "higher quality" cable, and two cheaper ones. All three work just fine, and in the end the cheaper, thinner ones were easier to fish. I DO think it is worthwhile to test-play a Blu-ray disk through each cable, after you fish them, but before buttoning everything up, just to make sure that the fishing process didn't harm anything.