Depends on the price of the original headphones as to if they're worth it or not. A lot of times companies will use this crappy wire that's half actual metal wire and half insulator inside to add strength to it, so soldering wiring can be a pain with them.
If they're $50 or under, easier to get a new pair, unless it's a really simple fix (new plug or something). Also, a lot of places usually offer some sort of replacement option for like $3-$5 for a few years, if they go bum get a new pair.