How did this phrase come to mean something positive? As recently as five years ago, I was hearing the phrase off the hook (though I usually hear it pronounced off da hoo’) used to describe someone who’s “lights were on but no one was home.” Now it seems to mean something along the lines of exciting or outrageous.
Is this simple bad-means-good, or am I missing something else at work? What’s next for describing a good time? 404? 
In my world “off the hook” means the same as “It didn’t happen on my watch, Chief.”
Suppose something bad has happened in my department while I was on the job. And further suppose that it looked for a time as if it had happened because I didn’t do something I should have done. However, upon further investigation it turns out that my omission had nothing to do with the bad event. I am “off the hook,” as when the hook is dislodged from a fish that seemed to have been caught.
Well, there’s two usages here:
(1) “You know that guy you’re accused of murdering? Turns out he took off to Aruba with his secretary and $15 mil he embezzled from the company. So it looks like you’re off the hook.” – here, the comparison is to a fish, as David said. You are no longer the prime suspect, the one responsible, the one who’s gonna have to pick up your brother-in-law at the airport if he can’t get a car rental (if he can … you’re off the hook).
(2) “That was the craziest party I ever went to. Joe invited all these hot models, there was food and drinks everywhere you turned, people were dancing their butts off… I’m surprised the cops didn’t come. I tell you, that dude Joe? That motherf—er is off the hook.” – here, I think the comparison is more to a phone than a fish. But whether b/c off the hook implies (a) you took the phone off the hook b/c you’re doing crazy things and don’t want to be interrupted (b) the phone got knocked off the hook b/c of your antics © you’re talking on the phone.
Off the hook can mean something good or bad. Depending on the context, someone can be acting “off the hook,” meaning that they are buggin’ out (to put it colloquially).
Nowadays (as you said) it usually means something positive, like “That new Jay-Z album is off the hook”
Anyway, its been used for awhile now, but it became especially popular after The Beatnuts multi-platinum single “Off the Books,” which contained this chorus/hook:
Other variations:
Off the Heezy (southern)
Off the Hinges
Those are valid possibilities, though I can hardly imagine today’s cell-phone-toting youth would ever consider any activity worthy of taking the phone off the hook. Option (b) sounds more likely to me.
The “not responsible” or “not accountable” meaning is certainly available, but that derivation does not confuse me. It seems clear to me that it is a dead metaphor, describing a situation in terms of a fish escaping capture. I’ve not heard the construction I’m asking about used to describe a person, only a situation (toadspittle’s example) or object (heard in the trailer for the new film Clockstoppers: “Yo, that watch is off the hook!” or words to that effect).
I don’t think it’s a recent expression - although I am only 20, I’ve heard it for years. And although I do have a cell phone, I still do have an old “hook” phone or two in the house (and even a rotary phone). The concept of a phone ringing “off the hook” is also often portrayed in movies, particularly on old phones where the bell is making the reciever shake. I think it has nothing to do with knocking the phone down due to some crazy antics, or taking the phone off to avoid calls, or because you’re already on the phone.
I hadn’t thought of that possibility. Good suggestion!
Don’t forget:
Off the heezle fo’ sheezle
Off the chain
Off the meat-hook
Off 5 hooks
Off the rack
and my personal favorite: off the tow-rope
To talk about a phone “ringing off the hook” is to say that calls are constantly coming in. As in, “Ever since that great story about our charity work appeared in the newspaper, the phone’s been ringing off the hook with people wanting to volunteer or donate.”
Conceivably this got mutated into something being exciting or outrageous or wonderful (just a guess).
Lighter(RHDAS) offers:
off the hook meaning “wonderful;exciting;impressive. From Rap Music.” First cited by LIghter in print in 1996(The New Yorker).
He does offer a possible link via the earlier(1990) term hooked. It meant “attractive, well put together. Her hair was hooked. 1994. Black talk Describes something or someone that is attractive, tastefully put together, upscale.”
Perhaps hooked was first, and then morphed into "off the hook.’