With the explosive adoption rate of Apple’s iPhone smartphone since its release a little over a year ago – more than 25 million phones to date – it couldn’t be long before researchers would start examining user behavior and study the most popular applications that are being used.

Indeed, there are already hundreds of “for free” and “for fee” applications that are available for use on smartphones.

So what are most popular iPhone apps? You’re to be forgiven if you think of music or games, because that’s certainly where most of the press hype has been. But in fact, the most popular iPhone apps are all about … the weather.

That is right. In a recent report issued by online market research and analytics firm Compete, staid and unexciting weather apps were cited by ~40% of respondents as one of the three top iPhone apps they used.

The next most popular application cited? Facebook (by ~25%). By contrast, game applications were cited as a top three-category by only ~20% of respondents, and music apps even lower still.

So much for iPhone users demonstrating cutting-edge online behavior!

In a related analysis, online analytics firm Pinch Media found that most iPhone apps aren’t setting the world on fire in terms of their popularity. The Pinch analysis found that iPhone users are quite fickle: Only ~20% ever return to a free app after downloading it. And a month later? The return rate drops to a paltry 5%. (The percentages are even lower for paid apps.)

These stats have implications for third-party advertisers on smartphone app programs. For many, it may make more sense to advertise on The Weather Channel or other less flashy but more frequently used apps than going with high-sizzle gaming applications that might be used only a handful of times before they’re replaced by the “next new thing.”