Here is an example: I hook up my laptop to my TV via HDMI, and the screen automatically switches to "projector only," and sets the screen resolution from the original 1366x768 to 1768x992, just a hair under 1080p (and there is no cropping, there is actually a black border around my desktop, because the resolution is smaller than the TV's.) I boot up Mass Effect 2, which runs at my original 1366x768 resolution in full screen. On my computer, it looks like this, but on the big screen, it looks like this.
It looks like I cropped the image myself, because the Fraps logo is partially cut, and that's because I did. I took two 5 second videos, one on my laptop's screen, and one on my big TV, and they were exactly the same, no cropping, even though I could clearly see the edges cut off while I recorded on my TV, so I had to manually crop the second picture and estimate where the edges of the TV were. It must be a setting I changed on the TV, because the game isn't actually cropped, the TV appears to be too small, even though it's not.
My video card is an NVIDIA GeForce GTS 360M, and I've used the desktop resizing feature in the NVIDIA control panel, but it doesn't help. The only resizing option on my TV is a Format button on the remote, which has 5 settings: "Full" (original,) "Just" (stretches the image horizontally,) "H-Fill" (just like "Just") "4:3" (Crops the image even more horizontally,) and "Zoom" (Zooms in on the center, cropping the image even more.) I'm not sure how this started, or why, but I'd like to know how to fix it.
P.S. the model TV I have is a Panasonic Viera TC-50PS14 49.9" HDTV, and the max resolution I can set for the TV through my computer is 1920x1080. I don't know if that helps clear anything up.