My dad has a built in entertainment center that is buit to accommodate an old CRT television. As such, the entertainment center itself is fairly deep (call it 24" or so), but the cavity for the television itself exposes a 24" high by 27" wide area. There is, however, a 2" overhang wherein the shelf on which the TV would sit stands proud of the cavity, extending further than the wall.
Looking at new 40" flat screen TVs, I see that the most common width appears to be something on the order of 32", meaning that any 40" TV I get to fill the cubby heightwise would extend beyond the cubby intended, and spill over into the cubby next to it.
Because of the 2" shelf, I see no problem if and only if I could somehow mount the TV securely.
Unfortunately, the sentimental value of the entertainment center is such that replacing it or even cutting it is out of the question.
I am considering 2 options:
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Mount the TV to a stud behind the entertainment center.
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Mount the TV directly to the wood (and it is real wood) of the entertainment center itself.
I don't like Option #1, because it would involve some really tricky mounting, in a small space, and the bracket would have to extend more than 2 feet to get the TV to stand proud of the cubby's side.
The question is, can one mount the bracket directly to the inside wood? It is real wood, although its only an inch thick or so. Is that enough? Alternatively, if I drilled through that shelf, but backed it into a sistered joint, would that hold?
This shows the short, clip style but it's available in 8' lengths too that you would cut to the length you need. 
but will still hold a fair amount (not much though). As for screws, they're often included with the kit but the same rules apply as previously discussed so if you buy a shelf package from Ikea or wherever and it comes with inch long screws or those plastic drywall anchors, do yourself a favor and go buy some real screws to mount it.
Best Answer
Another way:
Vesa MIS-C mount on the TV? Presumably the entertainment center shelf is designed to take considerable weight.
You could run a big L bracket down to the floor of the shelf, where you've installed a slot for the bracket to slide into and secure the display. Since 1" screws are unlikely to hold the full leveraged weight of the display, you could pile 50 or more pounds of weight onto the top of the slot structure. That should eliminate the possibility of your screws yanking out of the cabinet, and also eliminate your having to put screw holes in the, no doubt pretty, front of the cabinet.