Single-Link DVI can carry up to 1920x1280 signals. 1080p is 1920x1080, which means that pretty much any HD signal that you likely to be able to find in the next 10 years, can be carried over Single-Link DVI.
You only need Dual-Link DVI to run above 1920x1280. My Dell 30" LCD computer monitor is 2560x1600 - that requires Dual-Link DVI. The comparable Apple 30" LCD computer monitor is the same resolution, and obviously also requires Dual-Link DVI.
Any HD "television set" is going to top-out at 1080p. And in fact, any piece of HD consumer electronics equipment is going to have "standard" HDMI connections, which is electronically identical to Single-Link DVI (HDMI adds extra pins for carrying audio, and HDMI has a different connector than DVI, but the video signal is identical - DVI-to-HDMI adapters are simply pass-thru, with no electronics).