I own 2 sharp LCD's in my house. A LC-45GD4U and a LC-26DA5U. Neither accepts a 1080p signal, but you knew that

When I purchased the 45", the newer displays were not yet available. There was three different models, the 45GD6U, 45GD4U, and 45GX6U. the gx model had a seperate i/o box, with just 1 dvi cord going into the panel for all video. I guess there is a way to hook a 1080p source directly to this panel, bypassing the i/o box, to get a native 1080p picture. I guess it also required a dvi switch box, time, and patience. The success rate was not too high... there is a massive thread on AVS discussing this. As for the newer models, I don't know if they truly accept 1080p or not, but they are such small screens (especially the 37) that you might never notice the difference. I have been content with my 45" aquos, although there have been alot of flat panels released since I bought mine 8 months ago. The bravias should definitely be looked at... I haven't been very impressed with the sammys or toshibas, but there are always a million factors to take into account when comparing TV's, so your viewing experience may be very different.
If you have some basic technological know-how, perhaps you can find an older 45gx6u and do the hack... so at least you know there is a 1080p possibility instead of the newer models where everyone is still in the dark.
Honestly, I would have gone plasma, except I needed the anti-glare screen that comes with LCDs (there are way too many windows in our family room). Have you considered plasma? There are some good units that have dropped in price recently as the new models are being released.