Google Trends lets you explore the popularity of queries made through the search engine for any term - you can drill down to a specific time period and geographical region, even going down to a single city. The results are displayed in a graph, so you can see the rise and fall of interest in a topic. For example, here's the graph showing worldwide interest in the Diamondbacks.
The report is always scaled to a maximum score of 100, with everything else scored down from that - a score of 50 would mean search queries were at half the number of the peak. There's a natural ebb and flow along with the baseball season. In this case, the peak for the period covered (since the beginning of 2004) came in October 2007, as we marched to the National League Championship Series. Second place, perhaps surprisingly, was not our other play-off appearance in 2011 - that came fourth. No, with a score of 91, this honor goes to June 2013. It might have something to do with a little incident at Dodger Stadium, which took place that month.
However, for the purposes of this article, we're more interested in the results for Arizona. We're also making use of the Google Trends tool, which allows you to provide multiple search terms and compare them against each other - in this case, the four main professional sports teams in the state [I acknowledge the existence of the Rattlers and Mercury, but Trends caps you out at comparing five terms. I did check both, and interest was basically negligible compared to the big quartet] For time period, I chose since the start of 2007: this gives everyone a roughly equal spectrum of success and failure, with each team having two or three playoff appearances over that time.
Overall, the top three are very close to each other [sorry, ice-hockey fans!]. The average score for each team for the past eight years saw the Diamondbacks come out top, at 21, with the Cardinals close behind on 19, and the Suns there or thereabouts as well, at 18 - the Coyotes were well behind, rating a six. However, the top individual month belongs to basketball, the 100 score that marks the peak coming in May 2010. That was likely due to the infamous playoff series against the LA Lakers in the Conference Finals, including a loss at the buzzer in Game 5 with the series tied. This even beat the Cardinals Super Bowl trip in 2009, which was only an 85.
Interestingly, as far as in-state results go [as opposed to the worldwide ones above], the Diamondbacks peak came in September 2011, as we rolled towards the division title. That scored a 54, higher both than the post-season month  and the other play-off run, in 2007 - the latter was the D-backs worldwide leader, but in Arizona scored a 44. The Coyotes, meanwhile, managed to be the top team in Arizona for any month, just once, in May 2012 - not surprisingly, matching their first playoff series wins since moving to Phoenix, as they ran to the Conference Finals for the first time. Their score of 34 just edged out the Diamondbacks' tally for the same period, of 32.
This year's model
However, the graph above is just for 2014, and paints a radically-different picture - one that, perhaps, helps support the belief that Arizona fans are bandwagoners. For this year alone. the Cardinals are easily the most popular, with an average score of 29; the Diamondbacks come in at 22, with the Suns in third at 17, and the Coyotes down at 6. Our local NFL franchise took over as top dogs the first full week of August, and have largely gone from strength to strength since, with the past week being their most active. Depending on what happens the rest of the month, and how deep they go into the post-season, it could challenge their Super Bowl mark.
For the D-backs, you will be unsurprised to hear Internet interest peaked in the first week of the regular season at 49. After dropping precipitously for the first month, as our W-L record cratered in April, things stabilized through the end of June, dropped in early July, then rebounded for the end of the month before dropping to a in-season low of 19 for the week of August 17-23, and staying there as the season wound down. But how do the numbers compare year on year? Here are the figures for the four teams in each season. Note: due to the way these are scaled, you can only compare to other teams that same year. A 20 score in 2014 may not mean the same as that score in 2007.
Figures in bold indicate the team made it to their respective post-season that year. What we see is that every time there was a playoff team from baseball, football or basketball, they claimed the top spot (or spots, since in 2007 both the Suns and Diamondbacks made the post-season) for the year. It's clearly not coincidence, and is perfectly understandable - obviously, a winning team generates more interest. But it would be interesting to look at other states with a similar situation e.g. Colorado or Minnesota, and see if there's such a strong correlation between post-season appearances and local interest.