The '60's hippie universe is universe #420.
In Season 3's I Dated a Robot (2001), Professor Farnsworth tells Fry there are only two parallel universes: the primary universe and a cowboy universe. In this episode, there appear several more, meaning either Farnsworth was originally incorrect, or he (or someone else) managed to manufacture new parallel universes since his original comment.
First episode of the series to feature Professor Farnsworth's oft-mentioned "lengths of wire" serving a practical purpose. Farnsworth first referenced them in the pilot, Space Pilot 3000 (1999), albeit in that case they were shown in shorter lengths and hidden away in a special drawer.
When Zoidberg backs up against the shelves, the box containing Universe 25 falls over him, Universe 25 was a study carried out from 1954 to 1972 by John B. Calhoun, an American ethologist and behavioral researcher who claimed bleak effects of overpopulation on rodents were a grim model for the future of the human race.
The bookshelf containing alternate universes in Universe 1 that Zoidberg 1 upends has boxes labeled Universe 20 through Universe 39. Universe 25 - no eyes; Universe 1729 - bobbleheads; Universe 31 - robot versions; Universe XVII - ancient Rome; Universe 420 - hippies; unnumbered universes were leprechaun and pirate. Interestingly, all of the boxed universes shown reflect a version of the characters from Universe A and not Universe 1 where they were created.