Crossing dogs of other breeds with Poodles has become a bit of a phenomenon in recent days. Ideally, you get the best features of the poodle, the intelligence, the body shape, the low-shedding with the best features of the other partner. The most popular designer dog these days seems to be the Labradoodle, a Poodle and a Labrador Retriever combined.
The advantage of mixed breeds lies in the dog's health. Mutts tend to be less susceptible to health issues that plague pure breeds.
Unfortunately, giving a mixed breed a fancy name like Cockapoo (a Cocker Spaniel/Poodle mix) or Schnoodle (a Schnauzer/Poodle mix) makes some breeders feel like they have to also assign an outrageous price. Labradoodles can cost more than two thousand dollars in the United States! Chances are you can find an interesting mix of your own at a local shelter; give it a crazy name if it makes you feel better. My Boxer mix isn't a mutt; she is a Box-Pei (Boxer/Shar-pei mix).
Not all hybrids are a good idea. Mixing two dogs with respiratory problems, like a Pug and a Pekingese, can have disastrous results. Mixing two large dogs that are prone to problems like hip dysplasia, like a Newfoundland and a German Shepherd, could create a large problem.
Poodles seem to be the most popular candidate for designer mixed breeds. They are considered very smart dogs, and have the extra benefit of low shedding. Whether you are interested in an Aussiedoodle (Australian Shepherd/Poodle mix) or a Chinese Crestipoo (Chinese Crested/Poodle mix), you can probably find a breeder somewhere. Beware of amateur backyard breeders who don't exactly know what they're doing! Check the credentials of your breeders, and ask about the family history of the puppies.
Keep in mind that a designer dog, no matter what you pay for them, is a living thing and not a personal accessory. Make sure you are ready for whatever kind of dog you add to the family, you are making a lifelong commitment.