One of my dear friends buys almost everything D&D but reads only about 10% of what he buys. His goal is to have a complete D&D library.
Your dear friend has my commiserations. In the process of compiling a
complete index of D&D monsters I've accumulated a somewhat complete collection of D&D books. However, about 25% of my D&D library -- mostly older products -- consists of PDFs (back when they could still be purchased

), so I'm still a very long way from a complete
print D&D library.
Come to think of it, I'm not sure if there is now anyone on the planet who has a
complete print D&D library. For starters, there are number of
extremely rare D&D titles, such as
Up the Garden Path, a copy of which will set you back as much as US$2000 if you can find one. Which means the barrier to completeness starts rather high. There are a number of folks (perhaps a few dozen?) over at
The Acaeum who do have complete sets of early D&D products, but most of those collectors have not followed 3e or 4e (or even 2e in some cases). Similarly, I'm sure there are plenty of collectors who have complete 3e libraries, and even more who have everything for 4e. But I doubt any of the more recent collectors have copies of the original
Lost Tamoachan or complete sets of Dragon, Dungeon, Polyhedron and
Imagine magazines.
A complete D&D library is a mammoth undertaking. Even assuming that by D&D "library" we are talking about D&D game books and boxed sets, and not including the hundreds of D&D novels and comics,
dozens of computer games, thousands of miniatures, nor things like the Planescape
belt buckle, flask and key-chains, the D&D beach towel (of which there were apparently three varieties!) or the official
D&D Halloween costumes, we are still talking about a very large number of books.
WotC, by
their own admission do not have a complete D&D collection. I'm doubtful if there is anyone on the planet who does have a truly complete D&D library. Of course, if there is someone, chances are high that they read ENWorld, and will soon post in this thread

.