Yes, there was a time in their career when the fact that they were hatless was worthy of note. Men Without Hats hailed from the city of Montreal, where it gets very cold in the winter, but Ivan Doroschuk and his band refused to sacrifice style for comfort. (Ivan was actually born in Urbana, Illinois, but moved to Montreal as a child, and lives there still.) They were Wave 21 at first, Ivan and his brother Colin along with a dude named Jeremy Arrobas, and still in high school. They became Men Without Hats in 1977, and went through many personnel changes after that, some with another Doroschuk brother named Stefan, and with only Ivan as the constant.
In 1980, Men Without Hats had their first chance to go into the studio and record. They were almost purely an electronic band at this point, although Ivan had played some guitar at earlier gigs. The result was an EP called Folk of the '80s, which was released in Canada on Trend Records and in the U.K. on Stiff. In 1982, they recorded their first full-length LP and gave it the Soviet-sounding title Rhythm of Youth.
The big winner on the album was the track "The Safety Dance." Although it was an insistent little techno-pop tune, what really pushed the song over the top was the video, which went into heavy rotation on the year-old MTV. The video suggested a community-theater version of The Lord of the Rings, with Ivan Doroschuk as Aragorn and a dwarf named Mike Edmonds sitting in for all the little people of Middle Earth. Edmonds went on to play an Ewok in Return of the Jedi and appeared in a Harry Potter movie as well. I wouldn't make this up. The Safety Dance itself, as Ivan repeatedly demonstrated, was apparently this thing where you kind of made a box around your head with your forearms, making it one of those '80s would-be dance crazes, alongside the Bud Light Slide, that nobody ever did.
Released in March of 1982, "The Safety Dance" took its sweet time but eventually climbed all the way to Number Three on the Hot 100 in the summer of 1983. Ivan claims the song is really about pogo dancing, and how bouncers in clubs would try to keep people from pogoing because it was allegedly too dangerous. Thus, it's safe to dance. Everyone who heard it thought it was the epitome of a one-it wonder, so when their follow-up album, Folk of the '80s (Part III), arrived in 1984, no one expected too much of it. The lead single, "Where Do the Boys Go?," didn't make the Hot 100 at all, and only went to Number 30 in Canada.
But Men had one more trick up their sleeve. Their third LP, Pop Goes the World, was released in June 1987, and danged if it didn't have another hit on it in the title track. "Pop Goes the World" was produced by someone named Zeus B. Held - I'm guessing that's a pseudonym - and went to Number 20 in the fall of '87. Possibly even more intriguing from that album was a track called "On Tuesday,' which features guest flute work from Jethro Tull's Ian Anderson.
That success earned them the right to record another album, 1989's The Adventures of Women & Men Without Hate in the 21st Century. The single "Hey Men" made it to the Top Ten in Canada, but America yawned, and when it came time to make the follow-up, Sideways, from 1991, the Men couldn't even get it released in the U.S. That was really it for Men Without Hats, although they reunited in 2003 to make an LP called No Hats Beyond This Point. It's not clear to me if this ever really saw a proper release; according to Wikipedia, it was never sold in record stores.
In 2010, Ivan Doroschuk began performing with a group of heretofore non-MWH personnel under the Men Without Hats moniker, including a show at this spring's South by Southwest festival in Austin. It was apparently very well-received. Perhaps there's life for the hatless yet.