When I was a kid, I used to aspire to have a Schwinn bike. It was at least two steps up from a Huffy, which was what you found in a K-mart or other big-box store. Schwinns were sold at "Bike Shops," so they had to be good, right?
But, that was nearly 30 years ago, so I have no idea what happened to the brand in the interim. My hunch would be that the brand got sold to some other, cheaper, manufacturing conglomerate, if you're seeing them in Target.
Hmm, well, if Wikipedia is to believed, they did get sold - to China: http://en.wikipedia.org/wiki/Schwinn
Still is probably a good enough bike to get you from point a to b.