HDMI 1.4 can support 4K resolutions at 24bit color
HDMI 1.3 can support 2560x1600 at 24bit color
Dont forget that HDMI 1.4 and up officially supports 120Hz and 3D(1080p at 60Hz).
edit: Dual link DVI only supports UP TO 2560x1600
There is no product that i'm aware of using a proper HDMI implementation. Do you have a 1600p monitor? Have you tried using it with HDMI? Go ahead and try it. Have fun with that. Do you have an ultrabook with mini HDMI? Connect that HDMi port to a 1600p monitor. Again, have fun with your eyes bleeding from using a 1600p monitor which is now limited to 1080p at 30 or 60hz depending on your cable or outlet.
I have tried HDMI with every GPU i've ever owned, that includes 7970s, GTX 680, GTX 780, GTX 580, not a single one supports over 1080p through HDMI. I have to use DVI-D or displayport.
Anyone with actual experience with trying to use HDMI on a high resolution screen (eg 2560x1440 or higher) would attest to HDMI being junk. Furthermore, every ultrabook and HDTV implementation is 1.2. Every cable known to man is 1.2. That's the entire problem with HDMI, nothing is compatible with anything else and thus everything falls back to the lowest common denominator, 1080p. Some HDMI implementations don't even allow 60hz at 1080p. It's a joke. Furthermore, the cable has to be a certain spec, the output (eg. GPU or laptop) has to be a certain spec, and the monitor has to have a certain spec of HDMI. If anything is out of wack between the three, you again go to the lowest common denominator - 1080p at 30 at 60hz. Using HDMI with a high resolution screen is an exercise in frustration for this reason. Oh. Another point - HDMI 1.4 doesn't exist yet, nothing is using it. As far as i'm aware, using 4k resolution with HDMI involves 2 cables and you will be limited to 30hz despite using 2 HDMI cables.
HDMI is not a replacement or substitute for DVI-D or displayport / mini displayport as a PC display - Anyone using a 1600p monitor can attest to this fact easily. Again, i'm sorry for the in-eloquent language here but HDMI is garbage for anything but your HDTV. Until cable and panel manufactures can get their mess together, there is absolutely not a single reason for anyone to ever use HDMI for a PC. Unless they need the sound, or they're already at 1080p.