In the macabre Arkham Asylum: A Serious House on Serious Earth, which is a canon Batman comic, Joker slaps Batman on the butt and continually hits on him throughout the comic. Harley and Ivy both think that the Joker only has eyes for Batman (and Harley is in love with the Joker) and the Joker has often professed affection towards Batman (complete with moments of desperate attention-needing).
He's been romantically involved with multiple women, but also attracts a lot of Foe Romance Subtext with his male enemies.
