I’ve become interested of late in primitive music (I don’t know whether that’s the technically correct word), like African a cappella chorus and Appalachian bluegrass. Now, I’m ready to take on blues. Old blues. (Or new blues that’s like old blues.) I don’t know the term for what I want, but I’ll call it gutter blues. I want it rotten and nasty, with sweat dripping of the guy’s nose, and the veins in his neck popping from the strain of facial muscles. No watered down, modernized, melodic sissy stuff. Recommendations, please?
Skip James
Robert Johnson
Muddy Waters
Mississippi John Hurt
Blind Willie Johnson
Also, check out Ken Burn’s PBS documentary series “The Blues”
And, try Pandora.com. Enter the above names, and you’ll get all the blues you can listen to from all different acts.
You want Muddy Waters.
And you can’t beat Howlin’ Wolf.
Now those guys played “Chicago” blues with a band. For something more rural, try Son House.
For something a little more upbeat, Leroy Carr.
Skip James and Mississippi John Hurt sound like pretty much the opposite of what you describe.
Blind Willie Johnson and Son House are both especially great. Thanks!
If you don’t have it already, shell out for the reissue of Alan Lomax’s 1959 Southern music recording expedition, Sounds of the South. It’s fairly pricey, but it’s one of a handful of seminal recordings of Southern music. It doesn’t just consist of Blues, though. There’s tons of brilliant material to wade through. Let me also recommend (unless, again, you already have it,) Harry Smith’s legendary “Anthology of American Folk Music” collection. Again, not strictly Blues, and it may be a little difficult to get hold of. But this is the collection that famously kick-started Dylan’s career, and the entire Greenwich Village folk scene. Ask me, of course, the Village scene was a pale, pasty imitation of the original music. This collection is stellar, however.
While I’m at it, let me recommend any of the Deep River of Song series, which are reissues of the original Lomax recording trips (1938-ish). If nothing else, these preserve the works of Vera Hall, who was a natural vocal virtuoso from Livingston, Alabama. Remarkable talent.
Also of particular interest should be the back-catalog of Rounder Records, who have saved many obscure blues and roots recordings from extinction.
For present day blues that sounds old, I’d steer you to Keb’ Mo’ and Taj Mahal. I can hear the brickbats coming in before I say it, but don’t overlook John Hammond.
Overlook John Hammond. 
Also, I don’t mean to be elitist, but I’d be very careful with Keb’Mo and Taj Mahal. Keb’Mo has always seemed just a touch insincere to me…as if he’s aware that the music industry is looking to him to Carry The Torch. Plus, his stuff is far too overproduced for my tastes. YMMV, of course.
As for Taj Mahal, I think he has all the talent in the world, but his recordings are…spotty. Just really, really inconsistent.
If you want to know how to play the blues, get yourself a woman (Danko Jones).
For primitive blues it’s tough to beat T Model Ford. “PeeWee, Get My Gun” is the one I have.
Don’t forget Sippie Wallace. If you haven’t heard her yet, you still might recognize some of her songs – Bonnie Raitt covered Mighty Tight Woman and Women Be Wise on her first album. Bonnie’s good, but Sippie’s the real deal.
I like John Hammond and Rory Block, if you don’t mind white folks playing the blues.
I found Deborah Coleman to be one hell of a blues and guitar player.
Tripler
'Specially when she sings ‘bout throwin’ a “brick upside your head. . .”
Rhino put out a great series about ten years ago called “Blues Masters”. There were around twenty discs in the series. Each one covered a different sub-genre or regional division of the blues.
The series is not longer in print, but it’s pretty easy to find the discs online.
Lib, you trying to make me LIKE you? 
Usually “Blind” as part of the guy’s name is a giveaway, though some of them are mighty commercial. Another plug for Blind Willie Johnson, who is the most “primitive” I can think of that you can find easily is, except, being a preacher and all, could be more “gut bucket.”
The problems you will bump against are that blues weren’t recorded until well into the 20s (if you continue down this path, my son, you, too, will learn that the Day the Music Died was Jan 1, 1930) and that most of the singers wanted to be commercial successes. Robert Johnson, for instance, was more inspired by the work of Son House than any field hollers.
You will not regret buying the Harry Smith collection. You will hear all sorts of music; white, black, brown, and God only knows; not limited by commercial appeal, including Henry Thomas, whose work on the quills, a cane pan flute, was copied by Canned Heat in “Goin’ Up The Country.”
The accepted terms are “Primitive Blues” and “Primitve Negro Blues” if you can hack it.
I agree with most of what’s been said in this thread, although Keb 'Mo is basically the Kenny G of blues. Fuck that guy!
Here’s my favorites that haven’t gotten as much mention:
Blind Lemon Jefferson
Blind Blake
Memphis Minnie
Skip James
Son House
Leadbelly, of course (especially “Leadbelly’s last session,” where he’s just chatting with Alan Lomax, playing songs, chatting some more - really an amazing listen)
Charlie Patton
Definitely, most definitely check out the Alan Lomax recordings as mentioned, Harry Smith’s anthologies (don’t miss out on the lesser-known two-disc sequel anthology), the Smithsonian Folkways recordings, and so on.
If you find that you like this stuff, surely read Alan Lomax’s “The land where the blues began,” in which he chronicles his trips to the south with recording equipment in tow. Really amazing stuff.
Do any of the Lomax collections contain the "original " of “Black Betty” he collected for the Library of Congress? “Original” in quotes since I suspect it goes back a few thousand years.
You will be amply rewarded for checking out www.alligator.com where no recording ever goes out of print.
Hound Dog Taylor & the Houserockers ‘beware the dog’ was the first alligator record issued. he defines the electric primative blues. IIRC, also the only famous 6 fingered guitarist. he was simply awesome…