Depends on the animals. Cats are extremely low-maintenance. You could leave them alone for a week with an automatic litterbox and food dispenser. Or hire someone from Craigslist to check on them every few days. Some of them actually travel really well too, so you could always bring them with you. The main problem is finding hotels that'll take them, but you can always just sneak them in if they're not very vocal.
What I really don't understand is why so many people have dogs, and not just any dogs, but big dogs. There's no way you can get away when you have one of those things. They have to be walked at least once a day, they have to be let outside several times a day to relieve themselves (since they can't use litterboxes), if you live in a subdivision that means you need to accompany them outside so you can pick up the poo or else get fined (or you let them into your back yard and pretty soon the place looks like a Mad Max scene but with piles of dog poo all over), you can't easily take them on a plane (cats go in carriers under the seat), when you do take them they need a giant cage, and then frequently the pilot forgets to turn on the cargo bay heat so the dog freezes to death during the flight. The food cost is huge because they eat so much of it, so count on $50-100/month just for that, and on top of that now your house stinks and is filthy unless you invest a ton of time into constantly cleaning both the dog and the house (since they apparently can't keep themselves clean). You can board your dog when you travel, but that costs $30-50 per day, which adds up fast. Hiring a pet sitter from Craigslist is also doable, but most likely isn't going to work well because they can't visit often enough to let the dog out before it shits on the carpet or in his cage. You can't even spend an unplanned night at someone's house with a dog, because there's no way to arrange a pet-sitter that fast unless you have some very accommodating neighbors (and it's not good to assume they'll be around to take care of your dog at such short notice).