PORTLAND, Ore.—Two years after California voters rejected an initiative to legalize marijuana, advocates are promoting similar measures on the ballot this fall in Colorado, Oregon and Washington state—and recent polls suggest at least a couple of the campaigns have realistic chances of success.

Details vary, but all three measures would legalize possession of small quantities of the drug for anyone above age 21 and allow taxable retail sales, going well beyond laws in 17 states that permit marijuana use for medical purposes....