i will add i have done shows for/ had some bands stay with me who are fucking maniacs musically and onstage, but then are just totally normal dorks. youd be surprised!
Oh, and fucking Incubus. Loved Science, even Make Yourself and to an extent Morning View, but since they got rid of their original bass player (circa A Crow Left of the Murder) it's been one step towards throw away surfer bro-rock after the other.
Edited because i started ranting about music i hate, rather than, well, staying on topic.
Borknagar has songs about math and scientists and such. That probably qualifies. Although really I think we're working from about half a dozen definitions of square, so that it would be far more informative (and controvercial) to list bands who aren't square.
I think my definition of "square" is probably different from a lot of people's in this thread. To me, a band that is square is a band that was never relevant and never contributed anything thing to the musical landscape. Led Zeppelin, The Stones or Pink Floyd might seem lame now, but when they came out, they were anything but square. They might have produced bad shit towards the end of their run, but there are very few bands that stay cool all the way to the end.
Also I think a band is square when they are not self aware in some way. DEVO knew they were a joke from the get go, so it's hard to label them square. Now whether you think the joke is funny or not is another story.