I’m surprised this one hasn’t been mentioned – animator Bob Clampett’s farewell to Warner Brothers and Bugs Bunny – the Big Snooze is one long extended Elmer Fudd dream sequence:
A lot of places claim to have it, but I can’t get it to play. This one seems to work
http://www.trilulilu.ro/video-animatie/bugs-bunny-the-big-snooze
It has what looks like a parody of the dream sequence from Dumbo in it.
Fast Times at Ridgemont High. You know how cute Linda always thought Brad was…
Every time I hear “Moving in Stereo”…
No mention of the bowling and scissors sequence from ‘The Big Lebowski’?
Or maybe they meant Vanilla Sky?
You mean the one I mentioned in the OP?
“Heffalumps and Woozles” was the first thing I thought of. 
Some of the very first animated cartoons were suppose to be dreams. Winsor McKay, who (appartently unaware of parallel efforts elsewhere) independently came up with the entire mechanism of making animated cartoons, based his efforts on his own newspaper strips, two of which – Little Nemo in Slumberland and Dreams of the Rarebit Fiend, were ostensibly dreams.
His first effort, from 1911, features Nemo and two friends. Since they only appeared in dream sequences, the whole thing is arguably a dream (the film is hand colored!):
He himself made a couple of Rarebit Fiend dreams, The Giant Pet (which seems to be the first case of a Giant Creature Invading a City ever put on ffilm, predating The Lost World by at least five years and King Kong by 13. It even features an attach by biplanes!
The Flying House has a guy, threatened with his mortgage all coming due at once, fitting his house with a propeller and flying it off into space. I suspect (because of this, and other cartoons), that the folks at PIXAR watched a lot of McKay’s work, and stole this bit for their film Up.
https://video.search.yahoo.com/video/play;_ylt=A2KLqIX18jBV4UAASdb7w8QF;_ylu=X3oDMTByZ2N0cmxpBHNlYwNzcgRzbGsDdmlkBHZ0aWQDBGdwb3MDMg--?p=Winsor+mccay+The+Flying+House&vid=d9d5c674e208e8d1f0c676dc9f6ef619&l=6%3A19&turl=http%3A%2F%2Fts2.mm.bing.net%2Fth%3Fid%3DWN.%252b%252fxkUxKZHdLuiBCEB4hAcg%26pid%3D15.1&rurl=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D8sd9mHWCtLw&tit=Winsor+McCay%3A+Dream+of+the+Rarebit+Fiend+-+The+Flying+House+(1921)&c=1&sigr=11b8c1lvl&sigt=122094ov4&sigi=123gm898a&age=1379750574&fr2=p%3As%2Cv%3Av&fr=yfp-t-252&tt=b
There’s at least one silent short Dreams of the Rarebit Fiend that was done as a live action film, not a cartoon. I don’t know if McKay had anything to do with it directly.
Every scene with both John and Abigail in 1776.
My favorite Gilligan’s Island dream sequences were when Gilligan was Dr. Jekyll/Mr. Hyde, and when he was Dracula.