MichaelMeissner:
You want to make sure all connections are secure, since costumes can endure a lot of movement.
As far as secure connections, you can sometimes get away with using modular connectors, i.e. the connectors used for telephone and network cabling. They are cheap and widely available, but can still be pulled loose under some circumstances. Free hanging JST type connectors normally hold better and can be found various pin counts. In-line banana plugs and jacks are also possible, but can be rather bulky. The most secure option (and usually water resistant as well) would be to use circular connectors with an interlocking threaded shroud like this, but not only is it more expensive once you get above a few pins per connector they become awkward to use on most garments/costumes. Finally, if you are using conductive thread in a larger section of fabric it's possible to use clothing snaps as a secure connector.