Less than 16 months after it opened for business, the App Store now offers more than 100,000 applications for the iPhone and iPod touch, according to an Apple (AAPL) press release issued early Wednesday.

Two independent sites, AppShopper.com and 148Apps.biz, which track listings in the U.S. App Store, count 97,026 and 96,161, respectively. [UPDATE: A third, apptism.com, lists 100,699.]

Apple’s total includes 3,000 or 4,000 apps available only in its 76 overseas stores. Another nearly 9,000 apps have been approved by Apple but for one reason or another are no longer available for download.

The distribution of applications remains roughly the same as it was a year ago. According to 148Apps’ count, the U.S. App Store carries, among other offerings, more than 16,000 games, 13,000 books, 2,700 navigation programs, 1,200 medical applications and 442 weather apps.

Below the fold: A bar chart comparing the App Store’s 100,000 with the numbers available at the official application markets for Google’s (GOOG) Android platform, Research in Motion’s (RIMM) BlackBerry, Nokia’s (NOK) Symbian, Palm’s (PALM) Pre and Microsoft’s (MSFT) Windows Mobile phones.

Note, in some cases a lot more apps have been written for the platform than are available on its online store. For example, Microsoft’s Robbie Bach told PCMag last month that there were 20,000 Windows Mobile apps on the market; fewer than 250, however, are listed on Microsoft’s Mobile Windows Marketplace.

[Follow Philip Elmer-DeWitt on Twitter @philiped]