I'm feeling discouraged after getting tenure; should I quit?
Many faculty get post-tenure blues. There are several causes:
Burnout: You've been running at full speed for almost 30 years (k-12; college; grad school; post-docs; tenure track). Your brain needs a rest. It's perfectly acceptable for you to take a break. Many faculty have post-tenure slumps.
Survivor's guilt: Many of your grad peers didn't get jobs, you might have seen other faculty not make tenure. The tenuring process can seem capricious. You've just been through the sausage machine and you didn't like what you saw.
Imposter syndrome: Related to the above, you can't quite believe that you made it and you're doubting yourself. Were you really qualified to make it? Maybe there was a mistake in your file that they might catch?
Fear of commitment: You look at the other tenured faculty and are deathly afraid that you're now committed to be with them for the next 30 years. Oh god, what have you done. Your dreams of leaving academia and opening a bookstore-cafe by the waters of Lake Michigan are maybe just that, dreams.
Fresh fish: At many places, newly tenured faculty are fresh fish for burdensome committee assignments. e.g.: No one really wants to be the MA grad advisor but it has to be filled by a senior faculty member, thus the 'new guy' gets it. Some senior colleagues may actually tell you that you "owe" them because they "gave" you tenure. Bollycocks. You earned your tenure. You owe no one. Just try to remember the 'just say no' skills that you had as junior faculty and wriggle out of any and all commitments until you can figure out which ones you can tolerate.
Peter Principle: The Peter Principle ("people rise to their level of incompetence") is often misunderstood. It's not that you are incompetent, it's that you've been competent in one domain but promoted to a higher domain than where you've shown competence. Associate and full professors often have to do much more administrative work and intrauniversity politics than assistant/untenured faculty. When you're tenured, work becomes less fun and more bureaucratic. And you wondered why your senior faculty were all sourpusses. Key to your sanity here is to remain in domains that you're passionate about (teaching, basic research, etc.) and enter into new domains only on your own terms. For example, if the provost wants you to be chair of XYZ onerous committee, then you need $x research funds or to go to y conference or get z course relief (h/t to J and Captain Emacs).
Paradise Syndrome also known as the dog who actually caught the car syndrome. You've been working so hard for so many years for something you finally achieved and suddenly you don't know what to do with it. You have to come up with new life goals and purpose for living (thx Pharap).
The most important thing to remember is that they can't fire you without serious cause. Take a break, say no, piss some people off by not taking on work. Let your brain stretch. Go kayaking. Work on your bucket list. And then after that, try to remember what made you so passionate about your field.
Finally, if you really, really, really want to quit and you can't take sabbatical or get a grant to buy you out for a semester then: take an unpaid leave. The provost should be willing to work with you - if not, you can use FMLA or sick leave if you can get your doctor to agree you need time off. It's better than quitting as it leaves you with your Plan A when you recover.
It's hard to give concrete advice here because this is a very personal thing. First: It is quite common to feel empty when such a major goal have been achieved and probably you are left with no further major professional goals now. But face it: You don't need major goals in your life - smaller goals also work fine.
If you lost motivation to do research, I can recommend to try to enjoy doing science for the next time, and not focusing on the outcome too much. As a tenured academic it is one of your privileges to follow your scientific interests and not to worry about the outcome from the beginning. Pick simple problems, and think about them in simple ways. Also, talk to other people about your field and be interested in their work. This will give you insight in other areas but also new perspectives on questions you may already have.
Lastly, and to prove that you are not alone, here is another guy that felt the same. Although I usually don't like it to quote the famous guys on such problems, but it's written well and carries some good advice (but following it will probably not always lead to a Nobel prize as in this story):
Then I had another thought: Physics disgusts me a little bit now, but I used to enjoy doing physics. Why did I enjoy it? I used to play with it. I used to do whatever I felt like doing – it didn't have to do with whether it was important for the development of nuclear physics, but whether it was interesting and amusing for me to play with. […] I'd invent things and play with things for my own entertainment.
So I got this new attitude. Now that I am burned out and I'll never accomplish anything, I've got this nice position at the university teaching classes which I rather enjoy, and just like I read the Arabian Nights for pleasure, I'm going to play with physics, whenever I want to, without worrying about any importance whatsoever.
Within a week I was in the cafeteria and some guy, fooling around, throws a plate in the air. As the plate went up in the air I saw it wobble, and I noticed the red medallion of Cornell on the plate going around. It was pretty obvious to me that the medallion went around faster than the wobbling.
I had nothing to do, so I start to figure out the motion of the rotating plate. I discover that when the angle is very slight, the medallion rotates twice as fast as the wobble rate – two to one. It came out of a complicated equation! Then I thought, "Is there some way I can see in a more fundamental way, by looking at the forces or the dynamics, why it's two to one?"
I don't remember how I did it, but I ultimately worked out what the motion of the mass particles is, and how all the accelerations balance to make it come out two to one.
[…]
I went on to work out equations of wobbles. Then I thought about how electron orbits start to move in relativity. Then there's the Dirac Equation in electrodynamics. And then quantum electrodynamics. And before I knew it (it was a very short time) I was "playing" – working, really – with the same old problem that I loved so much, that I had stopped working on when I went to Los Alamos: my thesis-type problems; all those old-fashioned, wonderful things.
It was effortless. It was easy to play with these things. It was like uncorking a bottle: Everything flowed out effortlessly. I almost tried to resist it! There was no importance to what I was doing, but ultimately there was. The diagrams and the whole business that I got the Nobel Prize for came from that piddling around with the wobbling plate.
From "Surely you're joking, Mr. Feynman", by Richard Feynman
Just my two cents (I need to find a new introductory statement): I think it would be best to not necessarily quit, but reevaluate what it is that you are interested in doing at this point in your life.
Be it more research, being a more hands on/helpful professor, or heck, even shaking up the status quo at your institution (as there are a lot of aspects of campus structure that could use some shaking up, no matter the institution :P)
Find a new goal, now that you have attained one that takes a LOT of effort, time, and struggle.