The approximately 3-hour drive from Breckenridge to Aspen (2 hours due west on I-70, then under an hour southeast on Route 82) is absolutely stunning. First, upon leaving Breckenridge and emerging onto I-70, you almost immediately come to the Vail Pass which is beautiful: 12,000-foot mountains covered with snow tower above, and dwarf you so you feel almost invisible in their shadow. This lasts about 20 minutes, and then the terrain flattens out a bit and dries out to some extent as well.
After a while you hit a patch where looking northward are bone-dry, gorgeous red-rock formations shooting upward against the bright blue sky, and looking southward are the snow-capped ski resorts of Copper Mountain and other areas. It's pretty wild - two completely different terrains so close together!
Finally, about 2 hours west of Breckenridge you enter Glenwood Canyon, the home strech before you arrive in Aspen. This is truly one of the most breathtaking stretches of land through which I've ever driven. The bi-level highway that snakes through the canyon and criss-crosses over the Colorado River is a feat of architecture and a testament to the skills of its builders. The jagged Rocky Mountains shoot upward and almost engulf you as you drive along, and looking upward you almost lose sight of the sky, that's how big these mountains are. Tunnels shoot through the massive rock formations every now and then, and it's just astonishing to think about how they built a roadway like this through such imposing terrain, while barely disturbing its natural beauty.
I highly recommend this drive, especially Glenwood Canyon, if you are in the area. It goes by in a flash since there's so much beautiful scenery to enjoy.