I removed the lights on my Hampton Bay ceiling fan and there are two connectors, blue and white, that has "for light" written on it that are just hanging loose. What do I do with these? Do I just let them hang loose, or Can I connect them together, or Should I just put some electrical tape around them to cover them up?

Usually the live parts are protected by the plastic outer casing of the plug, but in case I am wrong or just to be sure, just wrap some tape around it before closing the cover.

DO NOT connect them together. Some fans have a plug and some have wire nuts on the end, either way is fine as long as no bare wire is showing. Wrapping some tape around as TK suggests is a good idea.