Mounting a TV up and out of the way above a fireplace seems logical, convenient, and undeniably cool. However, there are serious issues with such placement.
If you're planning on watching the TV only occasionally, that's one thing. But if this is your main TV and you're going to be watching it more than a few minutes at a time, beware.
If you're considering above-the-fireplace mounting, I'll presume you've already considered how you're going to run power and signal (HDMI or wireless) to the TV, and how you're mounting it to the brick/stone/whatever. These are concerns too, but easily fixable. There are bigger issues though, like...
Viewing angle (aka, 'The sore neck')
Ever sit in the front row of a movie theater? Some people like it, but most don't. That sore neck you get from staring up at the screen? Imagine that every time you watch TV. Most people find staring up at something for long periods to be uncomfortable.
Sure, some people in some rooms won't have an issue, but do you really want to be looking up for hours at a time. If so, good on ya, but you're in the minority.
Most of us would much rather look slightly down at a TV. It's a much more natural position.
Since most people buy LCDs (not sure why), there is an additional problem: most LCDs look significantly worse if you're not looking at them straight on. Even the few degrees below their centerline like you'd have sitting on a sofa looking up at the TV can be profoundly different than what it looks like on-axis.
The fix for this, if you're set on mounting above a fireplace, is a wall mount that pivots the TV downward. "Pointing" the TV toward the sofa is the only way to ensure picture quality with LCDs.
While plasma TVs are less susceptible than LCDs to off-angle degradation, some have screen filters, like Panasonic's "louvre" design, that can also dim the image when seen from extreme vertical angles.
Heat and soot
There is nothing worse for an electronics product than heat (OK, maybe water or kicking it could be worse, but you get my point). Increasing the operating temperature of the TV can shorten what should be a lively and reliably long life.
Worse, the soot from the fire can get into the TV's innards, doing nothing good.
Now, if you never actually use your fireplace, then you're fine. Otherwise, be wary.
Though stylish, mounting a TV above a fireplace isn't the best idea for the you or for the TV. Placement is a big issue, and location and TV height can be significant factors when it comes to picture quality. Check out "How to rid your HDTV of reflections" and "How high should I put my TV?" for more.
Got a question for Geoff? First, check out all the other articles he's written on topics like HDMI cables, LED LCD vs. plasma, Active vs Passive 3D, and more. Still have a question? Send him an e-mail! He won't tell you which TV to buy, but he might use your letter in a future article. You can also send him a message on Twitter @TechWriterGeoff or Google+.