Roundworms look like spaghetti noodles, they are disgusting. When I got Oscar he had roundworms and a couple came out in his sleep...uggghhh. Worms are easy to treat, just don't wait-tapeworms can be transmitted to humans...
The most likely culprit is tapeworms. They are white and flat, anywhere from ½ inch to 12 inches or longer, depending on how long the dog has had them. If you look at the dog's anus, you can see what look like grains of rice around the anal opening and/or stuck on the hair around the anus and on the base of the tail.
It could be other worms, like roundworms (I think those are white, but I could be mistaken).
But like I said, the most likely culprit is tapeworms, because if you get your dog wormed at vet visits, and you keep your dog on a monthly heartworm preventative like Heartgard, then intestinal worms are generally not a problem, except for tapeworms. Heartgard takes care of all worms except tapeworms. Tapeworms have to be treated with another wormer (like Panacur).
Tapeworms are caused by fleas. If you keep a monthly flea and tick preventative on your dog, you lessen the chances for the dog to contract tapeworms.