What makes a record collection "great"?

I have somewhere around 7000 LPs on the shelves that I've accumulated over many years, but I refuse to call it a "collection." It's simply my music library for what makes me happy and what I want to have available to listen to and to share with others.

In seriousness, though, all the things you mention differentiate various accumulations of LPs. For me, a great collection is one that gives great personal enjoyment. For my record library, it's about having superb performances, breadth and depth of selection, and many items with excellent sonics. But, that's just what makes me happy and what I enjoy sharing with other music lovers when they can come over. For some collectors, it's about having every LP in a given label's catalog, or every different pressing of a particular recording, or every recording by a particular artist... The list of different ways to define one's collecting bug is endless.

If you have LPs that you enjoy playing over and over, and if it keeps you happy, I agree with Slipknot: "I think you have a great collection."
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A "great" record collection, like a book collection, could include first editions of "classics" and limited editions. When I hold a first pressing of a "classic" record like an original Columbia "Kind of Blue" by Miles Davis or a rarity like the Beatles "Butcher" album, or a hard to find like a Nautilus lp edition of the Allman Brothers' "Live at the Fillmore East", than I feel I have handled history. Second editions, recent remastered reissues of classics are xerox-like copies of the original, good for listening, but not quite a "collectable". Whenever possible, get a first pressing of a "classic" or well regarded album because there's a reason why it is considered a "classic". Bottom line? Like everybody said, if you think it's great, it is great. (But it'd be greater if you have some "collectables".)

A 'great' collection isn't the same as a 'large' collection-for a collection to be 'great', it must be completest within it's own specific genre, including a historical perspective, and a large number of rare or unusual recordings. Let's look at, say, jazz. A great jazz collection would, by necessity, be a very large collection-tens of thousands, at least. However, a more specific 'Coltrane' collection, or 'Blue Note' collection, could still be great within it's specific subcategory, but require a library of far fewer recordings. Put another way, this guy http://superbizzee.blogspot.com/2009/05/ballad-of-record-rama.html who's been trying to sell his collection for years, supposedly has 3 million records, including 1 million lps. Without knowing the specific titles, all I can think of is that, in the long history of the lp, they put out millions of really, really crappy records.

just my opinion, of course. And for the record, I have a relatively 'large' collection, but nothing really 'great'-even though I 'greatly' enjoy it.

It's not the size that matters- it's how you use it.

It has your favorite albums