It's become a very popular thing to create designer dogs or hybrids. While there are a couple that have been around for quite some time such as the Cockapoo, most are relatively new. Examples of such dogs would be the Puggle (Pug+Beagle) or Labradoodle (Labrador+Poodle). Of course the Corgis could not be left out of this quest for a better breed and there are new models in the works as we speak (though none have caught on yet). I think Corgis are perfect the way they are and I'm sure others here would agree, but nothing is ever good enough for some. Here are some of the Corgi hybrids I've encountered. Please share any that you are aware of, or just voice your opinion on the topic of hybrid breeding.

Shorgi (Cardigan or Pembroke Corgi+Shih-tzu)

Copica (Cardigan or Pembroke Corgi+Cockapoo)

Others include:
Augi (Australian Shep. + Cardi or Pem Corgi)
Cava-Corgi (Cavalier King Charles Snapiel+ Pembroke Corgi)
Corgidor (Labrador+Pembroke Corgi)
Chigi (Chihuahua+Cardi or Pem Corgi)
Dorgi (Dachshund+cardi or Pem Corgi)
Corillon (Papillon+Pembroke Corgi)