You didn't say if it is a Schrader valve (like on a car) or Presta (the skinnier ones). Schrader valves are removable (with a cheap tool) and cost about $.50 each - good deal cheaper than a new tube.

Some Presta valves are replaceable, not all, and they cost about $1.50 each - starting to get closer to the price of a new tube.

Personally, if I have a valve leaking I just replace the entire tube. It always seems like the new valve stops the leak but not long after I get a leak around the base of the rubber where the valve stem goes into the tube.