Television auditions come in many forms. Cattle calls, open auditions, exclusive one-on-one's with casting directors, general casting calls, and sometimes a person is simply discovered while doing extra work or out on their evening bike ride (quite rare). One common element about television auditions is that they can result in you becoming stupendously famous as a well-known television actor! This is what you have to be thinking when you go on television auditions. Without this positive attitude, success will be much more difficult, and rejection will be that much harder to take.
Several people have gone on television auditions that were actually open auditions or cattle calls and ended up with a starring role in a major prime time television show. There is great potential for success in TV show auditions because television markets are so huge. Say you do land a starring role. Even if the show bombs and you have only been on television for a couple of months, your image has reached millions of homes. The upside of this scenario is that if, as is sometimes the case with TV shows, the show is picked up for syndication despite it's dismal performance opposite LA Law, you can now (if you had a good contract that didn't completely screw you over) sit back and watch those royalty checks role in!
Some people overlook television auditions, preferring to concentrate on the pursuit of film roles, but it's important to remember that many people have had rewarding and lucrative film careers that stemmed from a role in a television series that they got by hitting those TV show auditions hard and never giving up.