Apparently, the iPhone main menu supports only 10 screenfuls of apps. That's a mere 160 applications, including the 13 that come with it (and not including the 4 in the quick launch dock). Once you hit 160, additional apps you download don't show up anywhere and are not accessible until you remove some apps via iTunes. You can't delete apps directly on the phone to reveal new apps because it just leaves the empty spaces behind in the menu, and syncing again doesn't fill the spaces.

And you can't just leave empty spaces at the bottom of the last screen! Apparently, that just leaves an empty placeholder just as before. I was able to reclaim the empty slots by uninstalling then reinstalling the missing apps using iTunes.

Incidentally, rearranging the icons is a huge pain when many screens are involved. It's near impossible to move an icon two screens to the left without accidentally causing the icons on the intervening screen to move out of the way for your placing the icon you're holding. If that screen was full (16 items), this "move out of the way" action pushes the bottom-right-most app off the screen and out to the next left-most available slot—or App Limbo if all the other screens are full. And the spot left behind is not filled automatically, unless you "push" an icon on another screen to the left.

Anyone else hitting the 160 app limit, realizing what just happened, and regretting all 160 of them?