Wifebeaters are often worn by men known derogatively as "white trash", e.g. poor white people living in run down mobile homes. It is a common belief that such men are more likely to beat their wives, hence the name of the shirts which are named after them.

For more info, check out the wikipedia page:
http://en.wikipedia.org/wiki/Wifebeater_%28slang%29

I believe the term really came into popluar use after the advent of reality police shows, starting with "Cops". It seemed that, more often than not, when the police were called to respond to a domestic disturbance call they would encounter a drunk, dirty guy in his tank undershirt. It seemed to be a uniform of sorts for "wife beaters". And it was often the most noticable thing about the guy back when most of the accused had their faces blurred out on the screen.

Draw your own conclusions.

yayaya was right. After the play/movie Street Car Named Desire came out is when people coined the term "wifebeater". In the Marlin Brando wore that type of shirt and he was all sweaty, drunk, trashy and beat his wife. It's a classic. I remember studying that in a class in college.

Nobody in Oregon wears this stuff. It is too called, but we have plenty of trashy folks, one of them is an ice-skater.
-Vicki Pilcher from Oregon