My HR10-250 is currently connected to a non-HD 20" 640x480 LCD TV via component (480p). I also tried it at 480i with SVideo (looks about the same) and with composite (kinda blurry). So yes, it works with non-HD TVs just fine. You can adjust the output resolution with the remote or with the little button on the front of the HR10-250 box itself.
I used the included HDMI->DVI cable to connect the box to my 17" 1280x1024 Samsung LCD computer monitor. The picture was ok at 480p, a little squished at 720p, and really messed up at 1080i.
Speaking of cables, Kudos to DirecTV for including so many cables with the HR10-250!! Mine came with a stereo AV cable (composite), an SVideo cable, a component cable, an HDMI cable, and an HDMI->DVI cable. At BestBuy prices, that's over $120 worth of cables!!