"Side whiskers" generally, occasionally more colorful terms such as "me mate's got a full set of ginger brothers and sisters".

They became very fashionable in the early 19th century when civilians copied the dashing facial coiffures of the French Hussars. The Hussars were created in the 1780s and originally wore long braids of hair beside their faces, but adopted side whiskers when short hair was banned in the military.

Here are some contemporary quotes on the Hussars from the great Napoleon himself.

Edit: Meant to say "when long hair was banned". Thanks for the good catch, my fault.