Relatively advanced, though Federer, Sampras, and Agassi all won majors past the big 3-0.
Although he did win the 2003 US Open and finish 2003 ranked #1, it's somewhat a microcosm of his career that his two most memorable matches were ones that cost him major titles. Obviously, there was the 2009 Wimbledon finals, where he lost 14-16 in the fifth to Federer, and the win over Younes El Aynaoui in the 2003 Aussie quarters that went to 21-19 in the fifth set that left him spent for the semis.
In other eras, Roddick might have won multiple majors. I thought that, heading in Wimbledon 2003, he was headed in that direction. In the semifinals of Wimbledon, he faced Roger Federer, the 21 year old Swiss who, although ranked #4 in the world, didn't seem to have his best stuff at the slams. Indeed, he'd lost in the first round of the French just a month prior. But Fed ambushed Roddick with an amazing display of grass court tennis, beating him in straights. He reinforced his dominance over Roddick by defeating him in the finals of Wimby 2004, and also beat him in the 2005 Wimby finals, the 2006 US Open finals, the 2007 Aussie semis, the 2009 Aussie semis, and the 2009 Wimby finals. Whereas younger players such as Djokovic, Nadal, and even Andy Murray to an extent, have been able to reach the bar the Federer set, Roddick was never able to do it. In his prime, Andy's serve and forehand were world class, but his backhand, net game, and movement just weren't good enough. No one accused Roddick of not working hard, and he certainly tried everything he could to get better, but nothing seemed to stick.
In another era, he might have been revered. Instead, he found himself in the shadow of all-time great contemporaries AND his immediate American predecessors Agassi and Sampras.
Ah well- he has the 2003 US Open, a season-ending #1 ranking, 30 tourney titles, a hot wife, a bunch of money, and
one of the all-time great press conferences.
Godspeed, Andy.