The first-round pick sent to the Nuggets is lottery-protected in 2016 and 2017. It becomes two future second-round picks if the Blazers miss the playoffs in each of those seasons.
"Arron is a proven winner with playoff experience who will be easily integrated into our culture," Trail Blazers president of basketball operations Neil Olshey said in a statement. "He possesses a skill set that complements our style of play on both ends of the floor and will make an immediate impact as we continue our playoff push.
"Alonzo is an elite athlete and defender who adds a unique element to our perimeter."
The players dealt were among 39 to change hands Thursday, a day that marked the busiest NBA trade deadline day in 25 years.
The Blazers, who have been on the hunt for bench help, get a veteran shooter in Afflalo, who has been a bit of a disappointment since the Nuggets traded for him last summer. He is averaging 14.5 points, but is having his worst shooting season in seven years. He has the option to become a free agent this summer.
The Nuggets' goal in the deal was to acquire another first-round pick after they picked up two in a deal for Timofey Mozgov.
Barton, Claver and Robinson are all part-time players who are all scheduled to be restricted free agents after the season.
Robinson has verbally agreed to a buyout that will make him a free agent, sources told ESPN. It's expected to become official Friday.
Robinson, the fifth overall pick in the 2012 overall draft, is in search of an expanded role -- but that was not going to happen in Denver with Kenneth Faried at power forward and J.J. Hickson also in the mix.
ESPN.com senior writer Ramona Shelburne and ESPN Stats & Information contributed to this report.