Just a few examples from men v women at national team level (women's national team v men's national youth team).
18/12/2010 Latvia U-18 Men 29-0 Latvia Women (Latvia Women are one of the worst teams in UEFA)
23.04.2012 USA U-17 Men 8-2 USA Women (USA Women are essentially the best women's football team on Earth).
24.04.2014 Nigeria U-15 Men 1-0 Nigeria Women (Nigeria are generally regarded as the best women's football team in Africa).
Apparently, USA Women regularly played against men's youth and college teams in the past, as it was their only chance to play against teams better than themselves.
Also, in 2014, an amateur team from HMNB (Her Majesty's Naval Base) Portsmouth played Brazilian women's premier division side, Vasco da Gama in a 5-a-side challenge match. HMNB won 7-1.