Since April 2016, the RTD A Line is now in operation. This is a direct rail line from Denver International Airport to downtown Denver (Union Station).
The airport rail station is at the south end of the main terminal. There are trains every 15 minutes most of the day, going to every 30 minutes after 6:30pm and early mornings. There are departures from the airport until after 1:00 am. The journey to downtown takes 37 minutes with no transfers. Luggage racks are available on the train.
The regular fare is $10.50 and is sold as a day pass, including unlimited rail and bus travel throughout the RTD system for the whole day. Tickets can be bought at a machine on the platform using cash or credit card, or using a phone app. There are discounts for youths, seniors, people with disabilities, and certain other categories, but you may need to have appropriate ID or documentation.
(For marketing purposes, the line is branded as the "University of Colorado A Line". Its Union Station terminus is reasonably close to the University of Colorado Denver, but travelers should note that the line does not serve the university's better-known Boulder flagship campus.)
Market Street is three blocks southeast of Union Station.