IF YOU COOK, Other People's Kitchens are always adventures. The rest of the house is pretty predictable, and you've seen pictures anyway: Bedrooms have beds, bathrooms have towels, and living rooms have couches.
But no one shows you pictures of the interior of their cabinets. And if you're devoted to the culinary arts, when you get to someone else's house and you're planning on cooking for a week, that first look around may be thrilling, mildly satisfying, or crushingly disappointing. Is there nice cookware? Mustard? Cumin? Even garlic? Good signs. Are there a couple of decent pots with which you can make do? Olive oil? Vinegar? You'll live. Is there nothing—not even ketchup? It happens. (I swear, I was at a place last month that had been scrubbed so clean I had to go out and buy salt.)
There are two things you know, no matter what. One, you're going to have to go shopping. But you signed on for that; it's part of the fun. And two, you're going to wish you had brought a couple of knives with you. Because the cardinal rule of Other People's Kitchens (and it applies even to some of my friends' kitchens) is that they never have sharp knives. People may have late-night-TV bargains or they may have Wüsthofs, but chances are good that they have never sharpened either.
So that's my first and, really, only ironclad rule: Bring knives. (This assumes checking your bags, of course.) I bring a chef's knife and a paring knife, and I have never regretted it. A bread knife almost always comes in handy and, if you do a lot of walking, a pocket knife for cheese or whatnot is a good idea—but to me, two knives are minimal.
Beyond that, all traveling cooks must pack according to their personal needs. You can buy salt and olive oil, but those are things you'll probably find when you arrive in someone else's house anyway, so on that level, you might as well relax. And, especially in other countries, shopping for weird packaged goods is always a trip.
The real issues are things that you don't want to go without, nor would you want to buy them for only a week or so. In the hardware world, that might be a fancy corkscrew; for me, it's a decent skillet. (A lousy pot is not the worst thing in the world, but a lousy skillet can make life truly difficult, and I say that as someone who, for six months, wrote a weekly cooking column while either on the road or using a hot plate and a microwave.)