The "I'm feeling lucky" button is such a staple of its homepage that Google kept it there even though it didn't do anything useful anymore, if you have Instant Search enabled. That's because you get shuffled off to the results page as soon as you start typing.
The button simply pointed users to the new doodles repository for them to enjoy whatever doodle Google has showcased recently. Now though, the "I'm feeling lucky" button is getting
a new lease on life.
If you mouse over the button, you'll notice that it changes, at least in Chrome, to several other variations like "I'm Feeling Puzzled," "I'm Feeling Artistic," "I'm Feeling Playful," "I'm Feeling Hungry," "I'm Feeling Wonderful," "I'm Feeling Stellar," "I'm Feeling Trendy" and "I'm Feeling Doodly."
Each of those leads to a different Google site, for example the "A Google a Day" game, an image search for "nebulae," the Google Art Project, the Les Paul guitar doodle and so on. It's a fun way of discovering Google stuff you may not be aware of.