ayumi hamasaki Complete Live Box Set (all four DVDs)
This is rare IF COMPLETE, mostly because the last DVD was an exclusive that you could only get if you mailed in a little card that you got when you bought it. However this promotion has ended I believe.
appears
kanariya
Fly high
AUDIENCE
Daybreak
Surreal
These are categorized as rare because of the limited 300k availability of each of them. It's interesting to note that many of them are recuts. Kanariya and Fly high are some of the more difficult to find ones.
~previously unreleased version~ the other side ONE
~previously unreleased version~ the other side TWO
~previously unreleased version~ the other side THREE
~previously unreleased version~ the other side FOUR
Unsure about these ones, but I think they're a bit rare because of limited release.. but not sure.
Connected (German single)
Depend on You (German single)
These can easily be attained if you have connections, I think. I've seen some of them available on the Japanese HMV site, but then again, I'm not sure about some of the older releases. I know some users here have gotten them from people in Germany / Europe though..
NOTHING from NOTHING (single & album)
This is definitely one of the most rare Ayu items known to fans because it was from more than 10 years ago! Originals sell for 200USD+ on YahooJapan!Auctions.. They're crazy collector's items, but there're a lot of bootlegs out there so watch out :O
H (Digipack Edition)
Again, I think this was limited because it was a special rerelease in commemoration of the 1million+ sales of H. [A bit like the 24k Gold ver. of A..] but don't take my word for it. :x
ayu-mi-x Box set (13 LPs vinyl)
This had a limited release I think.. not a high one either.. [/unsure
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...hope I helped at all :x