The downtown core, LoDo, Civic Center, the Highlands and Capitol Hill are walkable to and from each other, and the free MallRide shuttle runs the length of the 16th Street Mall every few minutes. Beyond that, RTD light rail is genuinely useful — the W line runs west to Jefferson County, the E and H lines south, and the A line connects Union Station to the airport in 37 minutes. The L line tram runs up Welton through Five Points into RiNo.
Cycling is excellent: the South Platte and Cherry Creek trails together form a continuous, car-free network from downtown out to most directions of the city. Denver B-Cycle stations are scattered across the central neighborhoods. For trips out to the mountains, a car is essentially required — most rental companies are at the airport with downtown counters too.