Mapquest shows three main routes from Dallas to Denver and I've used all three. The main one is 799 mi (Dallas-Wichita Falls-Amarillo-Raton-Denver), but it has had some construction on the New Mexico portion for some time. It is mostly 4-lane but does slow down going thru some of the West Texas towns. It's probably my favorite route.
The second route is 882 mi following the Interstates (Dallas-OKC-Salina-Denver). Boring as far as I'm concerned, especially thru Kansas - miles and miles of the same thing.
The third route is 788 mi and the one used by some commercial traffic (Dallas-Wichita Falls-Amarillo-Dumas-Limon). This is the route used by busses taking skiers to Colorado. A friend of mine claims it's the best route with fewer hills and passes (she hates Raton Pass). It's pretty barren out in the OK panhandle and the roads there are a bit rough, but it is 11 miles shorter.