Your raspberries are just doing that comes naturally! Raspberries are self-replicating, sending forth new shoots each year, called primocanes, that will bear fruit the following year, then die. That's one of the cool things about raspberries; once you've established a patch, it will fruit for many years--even decades-- without buying new plants. Here's a short U Maine video about growing raspberries: http://bit.ly/10yFXoO
To get a good crop, and to keep plants from taking over the landscape, you need to prune your summer-fruiting raspberry patch every spring, cutting off the dead canes that bore fruit last year, and selecting the strongest live canes to fruit this year. Here's another good U Maine Extension video on how to do it: http://bit.ly/10yFvXH
Some varieties are especially exuberant in shoot production, so they'll keep you very busy pruning, since the roots keep sending out new shoots all season long.