Any social partner dance, really. "Ballroom dancing" may evoke mental images of old-fashioned dances in a formal setting, but there's a huge selection of different dances, some very modern and casual. West Coast Swing [1] is my passion. Its roots are in Lindy Hop, the grandfather of swing dances (and itself very fun to dance) but it's modern and smooth and sexy and mostly danced to contemporary popular music.
+1 on WCS. My only regret was not taking dancing lessons early. Guys, one of the easiest things to improve self esteem and to have fun at social occasions like weddings is to learn some basic dance steps. It's not as hard as it seems and the basic classes do assume you can't dance at all.
[1] https://en.wikipedia.org/wiki/West_Coast_Swing