It's amazing that this movie has had the same effect on so many people. Like several of you, me and my friends merely enjoyed Lebowski the first time we saw it. The second time I saw it, I liked it a little bit more, enough to purchase it (which isn't saying a whole lot considering what's in my collection). The third time, however, it hit me. The deliberate, methodical nature of the film, the genius of it, it just clicked into place and I absolutely fell in love, and I love it even more with every viewing. In fact, I'm hard pressed to think of a comedy I hold in more esteem.
It's the little things, like how when they're discussing how to get to the kid's house who stole the car they keep referring to how it's near the In and Out Burger. It's not something you'd normally notice. Then they go through the whole ordeal with the kid, and the corvette smashing, and then the scene cuts away to them driving away eating In and Out Burger... not outrageously funny, but about the 4th time I saw BL I remember bursting out into laughter at this scene after realizing the subtle intra-contextual reference.
Or how in the first scene, with The Dude in the grocery store picking up his milk, we see him glance at Bush on TV saying, "This agression will not stand", and then several scenes later he uses that same line on Lebowski in his office.
Or how when The Dude comes back to Lebowski's house, and Lebowski is in front of the fire, there's this very somber, dramatic music in the backgroud and you assume it's not diegetic, but when the Dude closes the doors on the way out the music is muffled because it was actually coming from inside the room.
God, I could go on and on about the little things (and big ones) I love in the film... but I demur for lack of time.