I do collect some authors but I collect series more than I collect authors. When it is a author I buy when something comes out new or when I find their books in used books stores. I never buy all of the books at once. If I find a series I like and it has been published for awhile I will buy all of the books at the same time. Most of the time I read the entire of the collection in the series. The exception is used books by romance authors. Those often get shifted to my TBR pile and stay until I get around to them.
Some of my favorite series are:
Mystery: The Lady Julia Grey Series by Deanna Raybourn, The Miss Tolorance Series by Madeleine E. Robins, The Captain Lacey Series by Ashley Gardner, The Sebastian St. Cyr Series by C. S. Harris
Paranormal: The Heart Series by Robin D. Owens, The Psy/Changeling Series by Nalini Singh, The Alexia Tarabotti Series by Gail Carriger
Science Fiction: The Lost Fleet Series by Jack Campbell, The Chris Longknife Series by Mike Shepherd, The Lt. Leary Series by David Drake, The Liadian Series by Sharon Lee and Steve Miller, The Confederation Series by Tanya Huff, the U.S.S. Merrimack Series by R.M. Meluch
I do own all of the books in the series I mentioned. Some of the books are on my comfort books shelf. Books that I reread that always seem new.