Some of the best web experiences are those that induce a sense of childish wonder in all of us, and probably the best fun web experience today is paperplanes.world. This site was "made by some friends at Google, Active Theory and Droga5" and it's thoroughly enchanting. The idea? You can throw and catch virtual paper airplanes, joining in with people from around the world.
Open the paperplanes.world web page on your iPhone, then tap the plus button to make a new paper airplane. You're asked to create a "postmark" (it will use your local IP address for finding your location unless you enable GPS) with your location, then get to "fold" the airplane with gestures. Finally, you use your iPhone to "throw" the plane, where it joins well over 700,000 other planes floating around the Earth.
On a Mac, you hear a nice electronic soundtrack and get to see where the planes are "taking off" from. On the iPhone, you see a virtual net that you can wave around to snag a paper airplane. Tap that plane when you've caught it, and you can see where else it has been captured.
It's totally relaxing and fun, so get throwing now!