There's many reasons that a cat could pant like a dog does.
Some reasons that could be causing your cat to pant like a dog are anxiety, excitement, fear and even overheating.
Sometimes your cat may be in distress as well when panting but if the cat doesn't pant all the time and only does it for a little while then your cat is likely okay but if he or she continues to pant like a dog then a visit to the vet is recommended.
If your cat has just been playing then it could just be catching it's breath after wearing itself out.