This article is from the X-Men Comic Books FAQ, by Kate the Short (firstname.lastname@example.org) with numerous contributions by others.
The Beast's normal form isn't fuzzy. Up until the cancellation of the
original X-Men series, he looked like a human with an ape-like body: no
fur, but big, elongated arms, hands, and feet. He had the same powers as
he does now: strength and agility.
Then, in Amazing Adventures #11 (1972), the Beast got a job at the Brand
Corporation, a subsidiary of Marvel's evil megacorporation, Roxxon. He
was researching the "genetic source" of mutations (the X-factor), and
isolated a hormone that would activate the X-factor. In typical comic
book timing, as soon as the Beast discovered this wonderful hormone, the
sinister Secret Empire tried to steal it from him. So Hank McCoy did
what any award-winning researcher would do with his potentially Nobel-
prize-winning experiment: he drank it.
The resultant enchancement of his mutant nature turned him into his now
famous fuzzy form, but with grey fur, and with a healing factor that
would shame Wolverine--bullet holes healed as fast as they were made.
Various misadventures ensued, until the computer Quasimodo drained the
Beast's excess life energy in Amazing Adventures #14, which left him not
only without his nifty healing factor, but also turned his fur blue.
He stayed that way all the way through his service in the Avengers and
Defenders until X-Factor was inaugurated. In their second issue, a story
was started which brought the Beast back to Brand, where much the same
sort of process left him back the way he was in the first X-Men series.
During the Fall of the Mutants he was infected by Pestilence (X-Factor
#19), resulting in a biochemical imbalance that increased his strength
each time he used it with a corresponding decrease in his intelligence.
A kiss from Infectia (#31) turned him back blue and fuzzy again, this
time with near-Hulk level strength (X-Factor #33).
Beast eventually lost most of that superstrength, and was back in his
"normal," highly agile, slightly-superstrong blue fuzzball form until
his lion-like form debuted in New X-Men #114. This was confusing, since
he was appearing in his normal form in the first issues of X-Treme X-Men
at the same time. However, in XXM #3, Sage first saw Beast's potential
mutated form. Just pretend that the events of New X-Men occur after all
of Beast's growing pains.