It hasn't been publicly announced by Apple, who like pointing out milestones that make them look great, but if you look at the stats over at unofficial iPhone App directory App Shopper, there are currently 101,751 approved apps available for the iPhone.
In August, we reported that there were 65,000 iPhone apps available. It took about 2 and a half months for that number to reach 100,000 - truly a remarkable feat. Have in mind that this is the number of approved apps; the actual number of available applications is a bit lower; according to App Shopper, it's currently at 93,035.
As far as the competition goes, it's hard not to rub it in. One needs only a quick look at (for example) Palm's App Catalog or even the powerful Nokia's Ovi Store to see where they stand compared to Apple's numbers. Windows Mobile has been around for over six years, and its Windows Marketplace for Mobile opened up a couple of weeks ago with 246 apps.