Ebay is also a good resource. Occasionally props and costumes from various productions will show up there.
If you want to rent a costume that you have seen in a movie or on television, you will have to find out what costume company supplied costumes for a production, which you can usually determine via the show’s IMDb page. Some of the bigger costume houses that you could contact about rentals are:
Angels The largest costume house in the world. They did work on Marie Antoinette, The Young Victoria and even Game of Thrones.
Cosprop has outstanding costumes. They outfit shows such as Downton Abbey and Mr.Selfridge
Tirelli Costumi has some absolutely gorgeous costumes from a wide array of films, including Cold Mountain and Jane Eyre.
Western Costume Company, which has been outfitting numerous movies in Hollywood for years typically has a big sale about once a year to clean out their inventory. Occasionally you can find some wonderful things there. You can also, of course, rent many of their costumes as well.
Lastly, Debbie Reynolds amassed an enormous collection of movie costumes over the years, which she has had to sell. The third part of the auction, through Profiles in History, is set to happen in May 2014. If you visit the site, you can sign up to be notified when the auction catalog becomes available.