I just bought a house that has an old concrete double basin utility sink. The right basin has a hairline crack and leaks water. I'd hate to sledge and remove it and was hoping this is fixable. Any suggestions?

There's all sorts of stuff for that: There are mortars, hydraulic cements - and even lots of stuff in tubes, like epoxy's and other "gunk" that are designed for concrete.

Glance around here:
http://www.quikrete.com/catalog/catalog_repair.html

... or go to Lowe's or Home Depot's Adhesives asile and you'll see tons of stuff.

Lots of stuff will work - so look closely at how the product looks when it dries. That may end up being what helps you decide which one is best.