Oh dude, absolutely! Almost any broken charger is broken because one of the contacts worked its way loose. And those are usually large, easy to hand-solder contacts. You can usually epoxy or glue the charger back together. It's a five minute fix and teaches you awesome repair skills.
This also works often for things like remotes and other small, cheap electronics. Contacts that broke or fell off the PCB (some wires are surface mounted instead of stuck through a hole).
Having said that, if you ever work with a charger that plugs into the wall: wear some sort of gloves when you take it apart. If you see a big capacitor - it looks like
http://upload.wikimedia.org/wikipedia/commons/9/91/Electrolytic_capacitors.jpg - put it back and don't touch it unless you know what you're doing.
And don't even think about taking apart really old TVs and monitors, since they often have huge capacitors that keep a 400V charge for
decades.
