Bart Centre says he'll be there. For $135 (plus $20 for each additional critter; PayPal accepted), he promises to look after your dog or cat or hamster or even llama once you are spirited away to heaven.
Centre started his company, Eternal Earth-Bound Pets, two years ago. But business didn't really boom until Harold Camping set the date of the Rapture at May 21, 2011.
http://www.npr.org/2011/05/21/136475372/after-the-rapture-who-will-walk-your-dog (http://www.npr.org/2011/05/21/136475372/after-the-rapture-who-will-walk-your-dog)