An iniquitous question, perhaps, but certainly there are mathematicians still living who are, for one reason or another, more widely known. It exposes my background, perhaps, but I would include Perelman, Wiles, Graham and Conway.
Who would you nominate for your current (or near current) top 10? Impossible, of course, since there are now more mathematicians living than have ever lived before, but it's a different twist than asking for the greatest ever.
Feel free to include nominations for "greatest ever" as well: