Although the Diamondbacks are hardly the first Phoenix team to host an All-Star event, the city hasn't had much history in hosting these events. The cause for most of that is the area's late growth; whereas many traditional cities have had significant population since 1900, Phoenix didn't start exploding until over a half-century later. As such, it hasn't had as much opportunity to even compete for All-Star events, but it has hosted some.
It should hardly be surprising that the team with the longest tenure in Phoenix, the Suns, have also hosted the most All-Star games. Phoenix has played host three teams for the NBA: 1975, 1995, and 2009. It's worth noting that the '75 game was the last game before the Dunk Contest was created, and that every NBA All-Star game logo for Phoenix featured saguaro cacti.
The WNBA selected the Mercury, one its founding members, to host the 2000 All-Star Game.
The Coyotes were slated to host a game in 2006, but it was scrapped when the NHL decided to not have All-Star games during Olympic years. Phoenix's year was pushed back to 2011, but was taken away with the significant financial problems the team has faced. It's unlikely the team will host one until it figures out its ownership problem, and it's reasonable to assume it will be a long time after that before one arrives in Glendale. The Carolina Hurricanes, who were the replacement host in 2011, were only promised a game after reaching certain milestones with season ticket sales.
It's not uncommon for the leagues to use All-Star games as an incentive for certain financial milestones. The NHL has used season ticket holders as a benchmark, and MLB has used new stadiums or renovations as the benchmark. Kansas City, who hosts next year in 2012, only was promised a game after undergoing a pricey renovation of their aging Kauffman Stadium.
Something interesting to note about previous All-Star games is the origins of the games. Baseball, being the first major sporting league in America, also had the first annual all-star game. Unlike some of the other leagues to follow, however, the first host was not one of the traditional powerhouse teams. In 1933 those teams would have been the Yankees (though only just barely, having just won its 4th championship in 1932), the Athletics, the Giants, and the Cardinals. Yet it was the White Sox who hosted the first game as a promotion for the World's Fair.
Contrast this with the hockey and basketball All-Star games' first hosts: Toronto/Montreal (depending on which game you take to be the first) for hockey and Boston basketball. Hockey had various All-Star games as charity events, but did not truly embrace an annual event until 1947, and its first few venues were all Canadian. The first American venue was Olympia Stadium in Detroit. The NBA's All-Star Game was not born out of such altruistic motives; it was conceived as a way to bring positive light to the game after a points shaving scandal in the college game. Strangely enough, the first two games were held at the Boston Garden. Sunny Los Angeles was the original venue of the NFL All-Star event, but when the league made it an annual contest the game was moved to Hawaii where it has largely remained. In fact, not only is the NFL the only league that regularly plays its All-Star Game at the same venue every year, but it is also the only one that regularly features a host that has never, and probably never has a hope of having a league team.
I'm sure if baseball had thought of it first, they would have hosted the MLB All-Star game in Hawaii; though given the general cheap nature of early owners, perhaps that idea would have died in the planning stages. It's not really apropos of anything, I suppose, but it's interesting that baseball held its first all-star game at a stadium not associated with one of the "great" franchises (no offense to White Sox fans, I have nothing against your team).
If we use the White Sox as our "model" franchise for All-Star hosting, then we need to savor the game next week in Phoenix. The White Sox hosted in 1933, 1950, 1983, and 2003. So in 20 or 30 years we might be lucky enough to see another All-Star Game hosted by the Diamondbacks. Chase Field will be 35-45 years old, assuming it hasn't been replaced yet. The city, the team, and maybe even the game, will all look different.
But nothing is guaranteed in baseball. The Mets haven't hosted a game since 1964. What will life be like in 47 years?