I have an old 20' racing sailboat where the outhaul is mostly missing. The wire is there at the end of the boom, but there's no rope coming out to cleat it. How can I run a new rope through the boom? Do I have to take it completely apart?
This will depend entirely on the type of boom and outhaul.
If you have a simple straight through outhaul:
If you have completely lost the outhaul, either get yourself a fish tape (from your local DIY store) or use a small plumb bob and fishing line.
A fish tape should work even when the boom is horizontal, but in order to use a plumb bob you'll probably need a couple of people as you need to hold the boom vertical to allow gravity to pull the fishing line through.
Once it is through, attach to your new outhaul and pull it through.
If you have a boom with internal pulleys to increase your purchase then you will find this much more difficult: