I mostly use 2 HDTVs for most all my games, a Samsung 48" 1080 and a JVC 32" 720.
I've only found a few consoles that have issues on the HDTVs (not counting the pal consoles, those I have a Pal tube TV)
1. Intellivision - For some reason the 1080 screen shakes real bad. But it works fine on the 720.
2. APF MP1000 - This obscure console will not work on any HDTV, I have to use a tube for it to work at all.
3. Pong Consoles - These are hit and miss, some work fine on the 1080 others only work on the 720 while others need a tube.
4. RCA Studio II - I can't even get a picture on the 1080, but it works fine on the 720.
I find it funny that these few consoles will not work on a 1080 HDTV while the 1st console ever made the Odyssey 1 works great on any TV I have. lol
I even have no issues with Japanese RF consoles where I have to turn the channel to Cable 96 to play it.
So if anyone is looking for a HDTV that works with classic consoles, I recommend a Samsung 1080 because if it's anything like mine, it will play all your consoles but the few I mentioned. But if your into lightgun games, you'll still need to drag out an old tube.
Just look at the back and make sure it has an RF, AV, RBG, and HDMI hook ups. (An S-Video input would be nice to, but not many consoles use this)