It's absurd, but I've done it myself. Then of course, there's trying to exercise in a foreign country, where you don't know what the heck lies around the next corner. So, if you're going running, bring a companion. If you go alone, you're the only dummy. Also, bringing a friend helps deter lewd remarks from sweaty foreign men with hairy knuckles, as you skip by.
Most hotels have at least some sort of exercise room.
However, most of them are usually pretty lame. If you are staying in a hotel that doesn't have an adequate exercise facility, try using common objects in your room to exercise with. The weight is just right to get a couple of good sets in. The phone book works good to put on your chest while you're doing sit-ups. If you're really motivated, throw the Yellow Pages on top of that.