I asked a question in the discussion section a little bit ago and got very productive responses. What follows is mostly a paraphrase of people's comments.

From time to time, like Pierre, I don't care. I get emotionally nihilistic. I find myself doing things that are morally awful in the conventional meaning of the word: procrastinating, sneaking other people's food out of the communal fridge, being casually unkind and unhelpful, breaking promises. I don't doubt that these are awful things to do. I figure any moral theory worth its salt will condemn them -- except the moral theory "I don't care," which sometimes seems strangely compelling.

What I want to know is: what goes through people's heads when they're motivated not to be awful? What could you tell someone as a reason not to be awful? If you are, in fact, not awful, why aren't you awful? What do you think, or feel, when you care about things? What would you tell someone who claims "I just don't care" if you wanted to get her to care? What would you tell yourself, in your nihilistic moments?

The (more) trivial utility function

Nihilism feels like a utility function where everything is set to the value zero. Landing that job offer or school admission letter? That's worth nothing. Making someone smile? Worth nothing. Being in good physical shape? Worth nothing. Living according to moral values? Worth nothing. Nothing is fun, or appealing, or worth looking forward to.

The thing about a nihilistic mindset is that you can't really argue your way out of it (at least, I've never succeeded.) It's perfectly logically coherent. A function that's constant at zero is still a function. You can have a function where all the best things in life, all the "peaks," matter much less to you.

Edit: Vladimir_Nesov comments that it's not really a zero utility function because even a nihilistic person doesn't behave totally at random, and can usually keep up some minimal degree of self maintenance. This is a fair point. It's more accurate to say that it feels like nothing matters, or at least that the desire for goal-directed behavior is significantly diminished. Maybe it's not a flat function, but a flatter function, where the things you used to value the most seem empty.

Most of us aren't in a nihilistic state all the time. But we can have days like that. Or weeks, or months, or years. (I had a year when I was almost always in this state.) And until you snap out of it, you can do a lot of damage, to your career, your relationships, your body, and your moral values. So how do you avoid all that?

Tactic 1: Get rid of the nihilism

Nihilism doesn't feel good. You don't have any positive emotions. The SEEK switch is turned off in your brain. It's really in your interest to escape this flat utility function.

So one thing you can do is to try to find a physiological switch. Take a nap, get some exercise, have something to eat. I've also found that what you eat matters: carbohydrates make me a bit more emotionally "down." Sometimes the physiological is enough. Sometimes you need a cognitive switch: start doing something absorbing, like reading a book or watching a movie or talking to a person. Because your motivation is very low here, you don't want to be ambitious. Do something that's easily available, or something that's already a habit. (I run enough on a regular basis that "go for a run" doesn't take much more motivation than "go to Subway and get a sandwich" -- but if you're not a runner, then running is a totally unreasonable choice.)

Tactic 2: Plan for nihilism

If this has happened to you before, and you know it could happen again, you need to anticipate and plan for those times when you can't bring yourself to care about anything. First, you need to prepare by "stocking up" on things that tend to help you escape a nihilistic mood. Keep the right kind of food easily available. Get adequate sleep over the long term. Make a habit of exercise (so that it's available as an option for you when you're "down.") Keep absorbing activities available: have books around you, and also have friends and social commitments that you can't easily blow off.

The other way of planning for nihilism is to have ironclad rules and habits, so that you can do pretty much the right thing even when you're not in a mood to care. Being rigorous when you're in a good mood should carry over somewhat to when you're feeling nihilistic. If you NEVER miss deadlines or play hooky, force of habit will carry you through even in your bad times. If you NEVER steal or make hurtful remarks, you're less likely to start when you get in a foul mood. Think of it this way: even now, you probably don't do just anything when you feel nihilistic -- it's unlikely that you murder people, no matter how bad you feel, because that's totally outside your range of possibilities. If something is totally outside your range of possibilities, if you normally never, ever do it, you're not very likely to do it for the first time when you're having a bad day. On the other hand, if something is an occasional vice of yours, you're liable to do a lot of it in bad times.

Tactic 3: Heuristics for escaping nihilistic thinking

These are things to remind yourself, or reflect on, that seem to be shortcuts to modifying your utility function away from flat.

Empathy. "How will this action make other people feel?" When you think about this, you may find that you suddenly care how other people feel.
Respect. "What would [person I respect] think of me for doing this?" You may find that you suddenly care about earning someone's respect.
The future. "Will I regret this later, after I've snapped out of my nihilistic funk?" You may find that you care about preventing harmful future consequences.
Awesomeness. "Am I being awesome?" You may find that you want to be awesome.

You may have your own heuristic -- something that reliably makes you care more, some kind of trigger.

Tactic 4: Avoid "rock-bottom rituals."

This didn't come up in discussion, but it occurred to me in my own life. Sometimes you have a "rock-bottom ritual," something you do when you start to feel terrible, that sort of cements the feeling. It's an official declaration of nihilistic misery. The prototypical example is drinking a lot. I don't do that -- I listen to Wagner and eat unhealthy food. You may have something different. The problem is, rock-bottom rituals prolong your nihilistic periods, when what you really want is to shorten them. Saying "Ok, it's time to break out the Jack Daniels" (or the Tannhauser and peanut butter) is just about the worst thing you can do for yourself.

Hopefully this will help. I'm still trying to figure out how best to manage emotional nihilism. It seems to be common, but it also seems to be more of a problem for some people than for others. I'd like to see any further contributions from LessWrongers!