Completist: Someone who wants to make something, such as a collection of books or records, complete. The OED puts it more strongly: “An obsessive (and often indiscriminate) collector.” And Encyclopedia Dramatica is even more judgmental:
A completist is a fanboy or fangirl that must prove their devotion to a band, television show, movie or comic book by collecting every piece of Chinese made crap sold at Wal-Mart that relates to said media. Symptoms include lining up at midnight to buy a new record, DVD, or toy, constantly searching eBay for imports of the same exact crap from Japan and camping in line for years just so they can get tickets to a show before you. There is a significant overlap between completists and fans of Pokémon and similar franchises, and this is expected given Pokémon's catch phrase “Gotta catch ’em all”.
Completist appeared in the first sentence in an article in last Friday’s New York Times holiday gift guide: “Completists with deep pockets can revel in the 2010 bounty of boxed sets.”
Merriam-Webster online gives 1951 as the date of the first known use of completist, but doesn’t provide a citation. The OED moves the date to 1955, citing an article in the New York Times Book Review: “Perhaps the one point of interest here, even for the Holmesian completist, is the effort in the introduction to identify Watson as Doyle’s secretary, Maj. Alfred Wood.”