The WAR leaderboards tell the story (click to embiggen):
FanGraphs OF WAR
Baseball-Reference AL WAR
By FanGraphs measures, Brett Gardner has been the fourth-most valuable outfielder in the American League. By Baseball-Reference's measures, Gardner has been the most valuable outfielder in the American League. That's not to say that either statement is 100% true (Mark Simon has some insight into Mike Trout's subpar dWAR), but it's impressive nonetheless. His all-around game has been stellar this year.
Gardner's superlative defense obviously gives him bonus points, but even if you don't trust defensive metrics that factor into Gardner's play like UZR and dWAR, it should be fairly obvious that he's a terrific outfielder. His defense has never been in question. His fine year with the bat puts him over the top.
Gardner has been hot lately, and due to an uptick in power, he might be hitting even better than he did in his six-win 2010 season. He's hitting .287/.349/.444 on the season with a 115 wRC+, a figure that might surprise to know ranks 11th in the AL among outfielders. Five of the outfielders ahead of him (Matt Joyce, Coco Crisp, Nelson Cruz, Adam Jones, and Daniel Nava) have negative defensive statistics, while Gardner's are fantastic. The 11th-best hitting outfielder in the league doesn't always go to the All-Star Game, but he should when his defense ranks among the best in baseball.
Gardner is a player whose defense merits at least one All-Star Game selection in his career. He's not sniffing the starting outfield through fan voting, which is unsurprising. However, AL All-Star manager Jim Leyland should strongly consider taking Gardner on his team to Citi Field. One could make an argument that he's been the most important part of this Yankees team that has fought through injuries to a 41-34 record. He's neck-and-neck with Robinson Cano in WAR, and for as awesome as Mariano Rivera and Hiroki Kuroda have been this year, pitchers can only affect so many games in a season. Gardner has appeared in all 75 thus far for the Bronx Bombers.
Cano and Rivera are near-locks to make the All-Star Game roster. Kuroda has an outside shot at a roster spot as well through a shiny 2.78 ERA that is sure to attract some attention. Gardner's defense sometimes goes under-appreciated, but his surprising offense in 2013 warrants at least a discussion of his All-Star Game candidacy. Although it's certainly an arbitrary honor, it would undoubtedly mean a great deal to Gardner himself. We can only hope that Leyland merely considers it.