One of the most accessible great hikes in the world, you can get to the trailhead on a shuttle bus departing Aspen every 20 minutes.
This is a great treat in a region where most trailheads are not accessible by public transport.
The 4-day circuit around the famous Maroon Bells (mountaineering peaks) is a classic. Most of the walking is above 11,000ft (3343m) so the views are magnificent.