I can really only speak for the breed that I know the most about, the golden retriever.
Line breeding can be very beneficial when done in the correct hands. Line breeding on one dog in particular can bring about the really fantastic traits in that particular dog and the ones behind it. Do it wrong, or on the wrong dog, and you can see undesirable traits show up in the offspring. A lot of kennels known for a "look" have done some line breeding to achieve that.
Where line breeding goes terribly wrong is in the hands of someone that doesn't know what they're doing. Someone that is breeding for "English Creme" golden retrievers. There is really no such thing. There are English goldens, bred to the standard in the UK. There are American goldens bred to the AKC standard. The "English Creme" does not belong in either. These "greeders" are breeding and line breeding on dogs for one reason, coat color. Well, everything goes to he11 when you don't breed for health, longevity, temperament. Grr.
Another issue is "popular sire syndrome" in certain breeds. One or two top winning and titled dogs sire a multitude of litters & before you know it, many many breeders are using them in their breeding program. Suddenly you have a bunch of dogs in the breed ring that are related. Not very diverse when looking for a dog with a complementary pedigree... when not line breeding.
Here is an example, Kirby, the top producing golden in breed history.
http://k9data.com/pedigree.asp?ID=19
A lot of responsible, hobby breeders will not breed to their own stud. If you think about it, it makes no sense. For one, what are the odds that you own the male that BEST complements your bitch out of all dogs in the breed? Slim to none. Someone doing this is more likely a back yard breeder, just my opinion.
Having a good database to research pedigrees and find the COI (coefficient of inbreeding) is also important for a breeder. In goldens, there is a website called
www.k9data.com. It is pretty interesting to see the genetic information and the 5 generation hip/elbow clearances, search via longevity, among other things. It really allows a breeder to see what dogs are heavily influencing a litter you're planning, or to see if any other get from the sire have had success in performance venues.