If your display/screen have a HDMI input you should have absolutely no problem to display any HD or Full HD resolution.
You can directly hook up and output 720p or 1080p from any HDMI source including :
HD-DVD and Blue Ray Player
PS3 and Xbox 360 HDMI
Any HDMI source.

If your display have a DVI connector, you have a few chances that it is DVI+HDCP in which case you will be able to directly input any HDMI source.

If you bought it brand new prior to 2006 , you have big chances that it is DVI only and not HDCP compliant, in which case you will not be able to connect a HDMI source to output 720p or 1080p

It’s a very common connector for PC monitor through which one a RGB signal is transmitted.
If you hook up a HD-DVD player, Blu-Ray player, PS3 or a HDMI graphic card, video will be downscaled to 520k at “best”, 960×540 instead of 1920×1080 !!
(DVD = 720 x 576p = 415K PAL/SECAM or 720 x 480p = 346 K NTSC )
Worst! Some editors or some hardware manufacturer will output a black screen (ex: PS3) even if, as they said “consumers will be extremely disappointed”