My Xbox is pretty funky.
It's a 20GB model, I assume no Falcon chip.
When I turn it on before I turn on my TV or I don't have it on the right video setting, I get RROD'd (this happened about a month after I bought it). However, when I turn it to the right video setting, I don't get the RROD, but it doesn't process the video to my screen. I then have to turn it off and then back on to get it to work.
So far, so good! Kinda pissed that I already got RROD'd. It has about 6 inches from the corner its in, and it is not covered by anything, so it's pretty interesting to me it's so picky like that.
Maybe it's the TV, as it doesn't like my SNES either..