First, a few notes. It is surprisingly difficult to track down final voting results. There is no one central location, and the links below go to about six or seven different sites. My Google-fu wasn't able to locate final numbers at all for 2004, so I used the last update, from two days before balloting closed. There is also no consistency in the number of players listed at each position, which can range from five to sixteen. Also, with outfielders being treated as a single class, I've taken their position and divided by three to compare with other spots e.g. 15th in the OF is equivalent to 5th anywhere else. Top performer is measured by fWAR for the first half of the season.
1998
Top vote-getters. SS Jay Bell + 3B Matt Williams (5th)
Top performers: OF Devon White (2.4), 3B Matt Williams (1.8)
All-Stars: OF Devon White
1999
Top vote-getters. SS Jay Bell (1st) + 3B Matt Williams (1st)
Top performers: OF Luis Gonzalez (4.2), 3B Matt Williams (2.9)
All-Stars: SS Jay Bell, OF Luis Gonzalez, P Randy Johnson, 3B Matt Williams
2000
Top vote-getters: SS Tony Womack (4th) + OF Steve Finley (7th)
Top perfomers: OF Luis Gonzalez (2.8), OF Steve Finley (2.8)
All-Stars: OF Steve Finley, P Randy Johnson
2001
Top vote-getters: 2B Jay Bell (3rd) + OF Luis Gonzalez (3rd)
Top performenrs: OF Luis Gonzalez (5.7), 1B Mark Grace (2.8)
All-Stars: OF Luis Gonzalez, P Randy Johnson, P Curt Schilling
2002
Top vote-getters: 1B Mark Grace + C Damian Miller (5th), OF Luis Gonzalez (8th)
Top performers: 2B Junior Spivey (3.1), OF Luis Gonzalez (2.9)
All-Stars: OF Luis Gonzalez, P Randy Johnson, P Byung-Hyun Kim, C Damian Miller, P Curt Schilling, 2B Junior Spivey
2003
Top vote-getters: 3B Shea Hillenbrand (4th) + OF Luis Gonzalez (14th)
Top performers: OF Steve Finley (2.7), OF Luis Gonzalez (2.5)
All-Stars: OF Luis Gonzalez
2004
*Top vote-getters: 2B Roberto Alomar (4th)
Top performers: OF Steve Finley (1.8), OF Danny Bautista (1.3)
All-Stars: P Randy Johnson
2005
Top vote-getters: 3B Troy Glaus (3rd)
Top performers: SS Craig Counsell (2.1), 3B Troy Glaus (1.6)
All-Stars: OF Luis Gonzalez
2006
Top vote-getters: None
Top performers: OF Eric Byrnes (2.3), 3B Chad Tracy (1.0)
All-Stars: P Brandon Webb
2007
Top vote-getters: OF Eric Byrnes (23rd)
Top performers: OF Eric Byrnes (2.3), 2B Orlando Hudson (1.9)
All-Stars: 2B Orlando Hudson, P Brandon Webb
2008
Top vote-getters: 2B Orland Hudson (6th) + OF Justin Upton (14th)
Top performers: 1B Conor Jackson (1.9), 3B Mark Reynolds (1.3)
All-Stars: P Dan Haren, P Brandon Webb
2009
Top vote-getters: OF Justin Upton (12th)
Top performers: OF Justin Upton (3.1), 3B Mark Reynolds (1.7)
All-Stars: P Dan Haren, OF Justin Upton
2010
Top vote-getters: 2B Kelly Johnson (6th) + OF Justin Upton (11th)
Top performers: 2B Kelly Johnson (3.0), OF Chris Young (2.1)
All-Stars: OF Chris Young
2011
Top vote-getters: SS Stephen Drew (5th) + OF Justin Upton (10th)
Top performers: OF Justin Upton (3.5), OF Chris Young (3.4)
All-Stars: C Miguel Montero, OF Justin Upton
2012
Top vote-getters: C Miguel Montero (8th) + OF Justin Upton (24th)
Top performers: 2B Aaron Hill (2.5), 1B Paul Goldschmit (2.0)
All-Stars: P Wade Miley
2013
Top vote-getters: 1B Paul Goldschmidt (2nd) + C Miguel Montero (5th)
Top performers: 1B Paul Goldschmidt (3.9), OF Gerardo Parra (3.3)
All-Stars: P Patrick Corbin, 1B Paul Goldschmidt
By any standards, it makes for spectacularly depressing reading. Between the last time the Diamondbacks had a player voted into the starting line-up - Gonzalez making it in as the final outfielder in 2001 - and Goldschmidt's runner-up spot last season, we didn't have anyone finish better than third. The highest-ranked player in All Star balloting over the decade-plus between 2002 and 2012 inclusive, including the division winning teams of 2002, 2007 and 2011, was Troy Glaus in 2005. Who was actually less valuable, by fWAR, to the team over the first half of that year than Craig Counsell. But DINGERZ, I guess.
I also note the relatively low performance of Justin Upton over the same time, never finishing higher than 10th in the five seasons he was a regular player with the Diamondbacks. Despite "Uptown", two All-Star appearances, etc. perhaps it's an indication of Upton's sometimes ambivalent perception by the fanbase - or certainly, some sections thereof. Certainly, it doesn't seem he was embraced in quite the wholehearted way every Diamondbacks fan seems to love Goldschmidt. In comparison, Upton came fifth in 2013 with the Braves, though you could certainly argue his extremely fast start (1.7 fWAR by the end of April!) was a factor in that improved ranking.
But at least things have been better than they were in 2006-07, when not one Diamondback was listed in the top five at any position, or among the top 15 outfielders. The latter is perhaps surprising; after all, we did win the division that year. However, we were only in third at the break, 3.5 games back of the Padres, and it was our second-half surge, going 43-29, that won us the title. This highlights one of the disadvantages of the system: it's less the 2014 All-Stars, than the "first half of 2014 All-Stars." Whatever you do after voting ends will be all but forgotten, by the time the ballot-boxes are opened next year.
Can Goldschmidt hold on? Damn, I hope so. He deserves it, by just about any measure. At 2.6 fWAR to date, he leads the league at the position, and is certainly more deserving than Adrian Gonzalez, who has posted a mere 0.9, and is back in 7th among NL first-basemen by that metric [amusingly, behind Mark Reynolds!]. But, y'know... Dodgers. In terms of performance, Goldie's closest challenger is actually the Cubs' Anthony Rizzo (2.4 fWAR), but he isn't even among the top five in voting. Indeed, no Cub is, and even the official site mournfully admits, "the team's representative may be a pitcher," with Jeff Samardzija and Jason Hammel among the top 10 by ERA.
Now, if you'll excuse me, I have to go punch some more ballots. #VoteGoldy.