Tweezers. (Some applications posted above come pretty close)

Keeping small and flat glue projects in place while the glue dries. (Obviously, this is pretty close to the original paper clip usage).

Unlock handcuffs.

Trade into a house (the story of One Red Paperclip)

WWII symbol of resistance.
Paper clip on wikipedia

The not quite true Norwegian national myth of the paper clip has been used actively as a symbol of Norwegian ingenuity. (The Norwegian inventor Johan Vaaler got a patent in 1901 for a simpler paper clip that was not quite as good as the modern paper clip. Don't let facts stand in the way of using a good myth...).