Many hotels welcome pets. Call ahead to see if your hotel is pet friendly. If you take your pet with you, you won't have to worry about hiring someone to care for it or place it in an unfamiliar place for an extended period of time. If you're going on an outdoorsy vacation, your pet might enjoy that kind of retreat.
Taking your pet along for the ride is only a good alternative when it fits your pet's temperament. If you've got a low-key dog or a cat, this option might be ideal. But you won't be able to kick back and relax if you have to worry about a puppy tearing up your four-star hotel room. You'll also want to take into account the distance you'll be traveling to your destination -- a long car ride or flight might stress out your pet.