When looking to for under counter TVs, for people who are trying to mount a small TV over their counter, or under their cabinets, there are plenty of models out there that will do exactly what they need. Most of the units, like those pictured above, have built-in digital tuners to receive television signals and inputs to receive signals from cable/satellite. In addition, a majority of the units come with a built-in DVD player.
The under counter TVs come with the hardware to install them. The units are fairly lightweight, thanks to the small LCD screens that come with them. And they are priced about the same as a DVD player itself, with the exception of some of the models with larger screens.
These types of units are ideal for watching television in the kitchen, where you do not want to take up space on the countertop for a TV and/or DVD player. They are also very useful in compact settings like Recreational Vehicles (RVs), boats or campers.
Because of the small size of the screen (generally under 12 inches), you won't want to sit too far away from the unit. Which is a good thing, because the poor-quality remote controls that come with under counter TVs is one of the biggest complaints about them.
The other major complaint about these types of under-cabinet televisions is the LCD screen failing to work. This is a spotty problem, but when it happens, of course, it means the unit is now worthless. The best way to avoid this is to make sure there is a good warranty on it. (This is true of ANY product with an LCD screen...the panels themselves cost more to replace than it does to buy a new unit.)
Christy - Under Counter TV info from http://undercountertv.net