-Great support for DivX and XviD, burned videos, etc. This would be 90% of the content I watch. 8% is burned discs in DVD format. 2% is actual, real discs.
-USB 2.0. I usually burn discs and throw them in my drive at the moment, but being able to buy a USB key would be nice and convenient.
-Good interface for file browsing a data disc or the usb drive. The DVD player I have right now is terrible for that. 6 letter or something restriction on file names.
As far as video, I'm not a nazi. I was robbed recently and they stole my TV, so I'm watching stuff right now on a 21" round tube CRT, so nothing would make a difference. I may switch to a 23" 1680x1050 monitor I have lying around extra. I may buy a TV in the future, maybe not, I'm ambivalent at the moment. If I did, it would be 32-40" 720p LCD, likely.
Multi-region or region free is a perk, sort of a tie breaker.
Price -- obviously cheaper is better all things considered. I'll spend up to $200.