Montenegro and Kosovo both unilaterally adopted the Euro in 2002; neither are EU members at present. For that matter, the Eurozone countries have given up their authority to regulate their own currency - though I suppose it's possible to argue that the decisions weren't necessarily made willingly.

Currency substitution is fairly common, particularly with the US dollar. There are less cases of full currency substitution (full legal tender, no domestic bank notes), but they do exist - mostly in Central and South America and the Pacific. The Caribbean Netherlands adopted USD in 2010 or 2011 IIRC, and Panama has used USD since the early 20th century (though I believe they use their own coins).