As far as game made for HD consoles with HD output, it was... Sonic 2006 on Xbox 360 lol. Which legitimately I loved at the time and I still am fond of it. I think at the time I even thought the graphics were good (yes, laugh at me), especially the character models, though I did not have an actual HD TV to play it on.
So the actual first game I played in HD though was I think Soulcalibur V on PS3. Yeah, I personally didn't have an HD capable TV for that long. It was nice finally being able to read text in games again, and I always thought the game looked nice even in standard def, so it was the game I decided to try first with the HDMI cable plugged in finally. I was like, "wow, yeah, this is much better, I get what people have been saying now."