How to ask a question to get an ordinal number answer

I'd go with the following structure:

Q: Where does Obama fall in the sequence of US presidents?

A: [He's the] 44th [president].

This reflects similar usage when discussing, for instance, rankings:

Q: Where did Harvard fall on the U.S. News & World Report list this year?

A: 2nd.

For a relatively well-educated audience, you might try:

What ordinal number represents the position of Barack Obama in the succession of US presidents?

This is quite a tough question. My suggestion is:

• How many presidencies preceded Obama? 43
• Including Obama, how many presidencies have we had? 44
• Which president count does Obama have?
• What's the chronological number of obama as a president of America?

I hope I could help you a bit

In the numerical listing of Presidents of the United States, what number was Obama?

or shortly

What number is president Obama?

I heard the latter from Jay Leno while he was asking this to a girl in his show.

Another alternative, as suggested in comments given below, is:

What number president is Obama?