A DVI switch.
Most HDTV's equipped with DVI/HDMI will also have at least one set of HD-compatible component video inputs and your digital tuner box should have a component video output option for HD. I would suggest leaving the Denon connected to your TV via DVI to take advantage of it's upconverting feature on DVD's, and connect your DirecTV digital box via component video. Although component video is an analog connection, in my experience it will still look fantastic on HDTV content.
I own the Samsung T-160 DirecTV digital tuner and have compared it's digital DVI out to it's component video out into my 34" sony xbr-800 direct-view HDTV and could not tell a difference on HD content. (for reference: my DVI cable is a Monster 400 and the component video is AudioQuest YIQ-3).
Your results may be different on a big-screen plasma, DLP or LCD, however. But it's worth a try before investing in a DVI switcher, and besides your next A/V receiver or processor will likely be able to switch DVI/HDMI much as most receivers will switch S-video, etc. today. Cheers! JZ