Dumb as a doorknob.
In our family, the expression was “both hands and a flashlight.” Funny, isn’t it what parents come up with? 
A classic one from Foghorn Leghorn:
“That boy’s about as sharp as a mashed potato sandwich!”
…and another from the olde south:
You put his brain on the edge of a razor blade and it would look like a bb shot rolling down a four lane highway!
“He’s only got two brain cells, and they aren’t on speaking terms.”
The wheel’s still spinning, but the hamster’s dead.
So-and-so has the intelligence of a piece of toast.
Sharp as a bowling ball.
(S)he’s so stupid, when (s)he walks into a room, the collective I.Q. drops.
If brains were candy, you’d have a lot of unhappy trick-or-treaters. (A Syko-ism, especially good for use arond Halloween.)
[Mr. Anderson (from Beavis and Butt-head)/]
That boy ain’t right.
[/Mr. Anderson]
(Did I do the “other person’s voice” thing right? It was my first time.)
-Syko
“So dumb he’d fall into a barrel of tits and come out sucking his thumb.”
“So few brain cells, he knows them by name.”
Or to describe someone who is physically attractive while mentally challenged:
“Nice cage. No bird.”
From my grandfather:
He ain’t got the brains the good lord give a squirrel.
He don’t know whether he’s pitchin or catchin.
He’s all vine and no 'taters.
Stupid as a stick and twice as ugly.
I sure do miss my Pawpaw! One time he was talking about a guy I was seeing. He said, “The only spark that boy’s got is from the rocks crashing together in his skull.”
And ya know, he was right.
dumb as a barnacle
(ask Wind Sorceress or Dragon Shadow…)
Fell out of the Stupid Tree and hit every branch on the way down.
don’t make him/her think, it’ll blow out his/her brains
::“not the sharpest tool in the shed”, followed closely by “not the sharpest knife in the drawer”
As think as [James Joyce’s] Ulyesses and half as intelligible.
His brain is like the South Boise Specticled Weasel Hawk – non-existant.
Dumb as a porn star but with more natural ingrediants. (Think about it.)
Think eyes are open, the mouth moves, but Mr. Brain his long since departed. (Blackadder II)
Always said that as “dumb as a post.”
(maybe even this one :))
The last post reminds me of an incident that happened some years ago. I was over at my friend Sarah’s house and she had invited a bunch of people, including our close friend Eric. I was schmoozing around in her room with Eric and a few other people and I happened to pick up a book entitled “Things That Never Were”. Meanwhile Eric had made a cheap joke about my studiousness that wasn’t terribly funny…but then, I said aloud, in a drawl:
“‘Things That Never Were’, hmm…now, lets see(flipping through book) ah yes.(Pointing at page)…ERIC’S BRAIN!”
'Twas funny. I dunno if it fits in with this thread or not but I assume you fellow Dopers will flame my socks off isf you judge it not to. Do your duty. 
“If his brains were dynamite, it wouldn’t be enough to blow off his hat”
“Truly unhampered by the ravages of an intellect.”
“He’s got two braincells left, and they’re bouncing around looking for each other”
He’s as numb as a pounded thumb
“X had a thought once, it died of lonliness.”
“The mental agility of a small piece of furniture.”
“His little choo-choo has derailed.”
Another version of this, If brains were gunpowder he couldn’t blow his nose.