Picking a favorite blues artist and tune seems a little out of keeping with the spirit of the blues. It's sort of like asking a person if he considers himself to be an existentialist. (If he says "yes," you should immediately suspect something since existentialism resists definitions.) But I'll take this in the spirit of it being an opportunity to share some interests with fellow blues lovers.
Three tunes come to mind immediately: "Devil Got My Woman" by Skip James, "Tell Me Where the Road Is" by Guy Davis, and "Prisoner's Talking Blues" by Robert Pete Williams.
There is only one really bad answer so far: the one that says there are only three blues singers "that matter." What in the world could that possibly mean? Of course the ones he names "matter," but so do many, many others.
Just some of my favorites (in additions to the three mentioned above): Mississippi John Hurt, Rev. Gary Davis, Son House, Robert Johnson, Lightnin' Hopkins, Howlin' Wolf, Stevie Ray Vaughan, Albert King, B.B. King, Bo Carter, K.C. Douglas, and on, and on.
By the way, I strongly suggest that anyone interested in this question at all become familiar with the allmusic.com website. The link below is to the beginning of the section on the blues (fifteen plus articles on country blues alone!). You can look up information by artist, genre, album, song, whatever.
Finally, please don't mess things up by proclaiming someone to be the "greatest blues artist of all time." This really doesn't help anything. This isn't a competition. And most of us weren't alive to see and hear some of the greatest of all time--and some of them were never recorded.
EDITED ADDITION SEVERAL DAYS LATER: Apparently there are three to five people going through and giving a "thumbs down" to every single answer. Do any of them care to answer the question and explain why everyone else deserves criticism?