You can tell by the equivocal title that I'm not a BIG King Crimson fan...so why would I "buy anything?"
I don't so much ENJOY the band as I respect their MUSICIANSHIP. Much of their music is sheer wankery, but it is technically brilliant wankery, even if the spectacular fireworks are little more than ear-candy or flat-out "showing off."
There are many King Crimson songs that I like, of course, but for the most part I buy their albums to hear Robert Fripp and his hand-picked bandmates go "look at what we can do!" Crazy tempos, micro-managed song-structures, elaborate fret-picking, Chapman Stick, over-the-top production, unconventional instrumentation...well, that's all pretty nifty but it doesn't necessarily make for "great music."
They started off in the late '60s mixing prog rock and highly-structured jazz, occasionally dipping into saccharine psychedelic folk. In the '80s they picked up Adrian Belew -- have I mentioned that I'd Buy Anything by Adrian Belew? -- and started doing adult contemporary art pop that I find ultimately forgettable.
I like their subsequent music much more: extremely heavy, noisy, somewhat discordant angst that probably got them their gig opening (!) for Tool. Here's their "double trio" act from 1995 performing "B'Boom" and "THRAK." Warning: sheer noodling on display, but it's meticulously rehearsed and sort of awesome. I think Belew is using some sort of MIDI guitar device.
Albums to buy: "In the Court of the Crimson King" (their debut) is pretty darn good and probably the highlight of their early period, but I personally like "The Power to Believe." Albums to avoid: I'm not a fan of "Starless and Bible Black" but apparently I'm a minority. For fans only: I don't think you even dabble in King Crimson unless you're already a fan, but I think TRUE fandom would be to watch the '80s concert videos without getting distracted by Belew's terrible clothes. I am unable to do so.