DENVER—Maintenance backlogs, budget shortfalls and breakdowns plague many of the U.S.’s aging transit systems. But here, where the plains meet the Rockies, Denver’s system is a rare success.

Created in 1969, the Regional Transportation District operated for years as a modest bus service, and in the 1990s it added a few rail lines. But in 2004, voters in the eight-county region approved an additional 0.4% sales tax to expand the train network, called FasTracks. That new funding dramatically boosted a stream of local tax money...