Though Bill Clinton's waggish reply - "First Laddie!" "1st First Gentleman!"- is
more a confirmation of his political professionalism (make a joke, reach out to wavering voters of Scottish ancestry) than useful, it is a question he will have to consider if Hillary makes it to the White House.
First ladies of yore took their time: not until 1877, nearly 90 years after George Washington became the first US president, did they settle on First Lady, having called themselves "Lady", "Mrs President", "Mrs Presidentress", even "Queen". But these days it would be a dereliction of duty if a tabloid journalist did not come up with a name for him in the first 24 hours - so Bill would be well advised to get in first.
There have been several non-wives who served as "first ladies." Presidents Andrew Jackson, Martin Van Buren, and John Tyler all had wives who died either before they were elected or while they were in office. In these cases, a close female relative, like a daughter or a niece, took on the position. James Buchanan was the only president to enter and leave the White House as a bachelor. He adopted his orphan niece, Harriet Lane, and appointed her to handle the First Lady's business.
The most generally suggested term is 1st First Gentleman. As that's also what the husbands of the female governors of Michigan and Alaska call themselves, perhaps they could gracefully step aside. Other countries have ducked the issue - in Ireland, Mary McAleese's husband is generally called Dr Martin McAleese, the president's husband; Angela Merkel's spouse, a quantum chemist, is so unwilling to have anything to do with her job that he was once nicknamed "the Phantom of the Opera" by the German press. But both the Philippines and India have First Gentlemen, so maybe Bill could join them, and make a club of three. Just so long as he's not called First Partner. Or, heaven forfend, First Spouse.