Technically, it all depends. In a lot of their shorts, they're just endless lovers, but if we're walking voice actors and alter egos, both the current voices (Wayne Allwine & Russi Taylor) and the original voice actor & the characters' alter egos (Mr. & Mrs. Walt Disney) are/were married in real life.
Plus, Walt himself put it best:
"In private life, Mickey is married to Minnie. A lot of people have written to him asking this question, because sometimes he appears to be married to her in his films and at other times, he's still courting her. What it really amounts to is that Minnie is--for screen purposes--his leading lady. If the story calls for a romantic courtship, then Minnie is the girl; but when the story requires a married couple, then they appear as man and wife. In the studio, we have decided that they are married...Really."
Note: Also, in House of Mouse, Mickey mentions his and Minnie's anniversary, which may imply that he and Minnie are married.