OK I cheated and used google and found (60 chars):

  for i in range(1,101):print'FizzBuzz'[i*i%3*4:8--i**4%5]or i

Pastebin of my explanation: http://pastebin.com/raw.php?i=00Db30FF

EDIT: ugh, sometimes I hate markdown, moved post to pastebin.

Awesomely ingenious use of math above. 59 if newlines count as 1.

    i=1
    while i<101:print'FizzBuzz'[i*i%3*4:8--i**4%5]or i;i+=1

Much simpler solution in 59 chars

  n=1
  while n<101:print'Fizz'*(n%3<1)+'Buzz'*(n%5<1)or n;n+=1

I came up with a shorter way to write the first index!

  n%-3&4

unbelievably it works

haha, clever!

Should have been empty string f[4:4]

Some simple ways to cut down on characters:

    for i in range(1,101):print 'FizzBuzz' if not i%15 else 'Fizz' if not i%3  else 'Buzz' if not i%5 else i

for i in range(1,101): print "FizzBuzz" if not i % 15 else "Fizz" if not i % 3 else "Buzz" if not i % 5 else str(i)

Even a little shorter :)

And a bit shorter still :D. Down to 102 chars now.

    for i in range(1,101):print "Fizz" if not i%3 else '' + "Buzz" if not i%5 else str(i) if (i%3) else ''

Edit: Down to 82 characters now. I'm not sure if this would work on every Python, but it works on mine.

    for i in range(1,101):print(("Fizz"if i%3==0 else'')+("Buzz"if i%5==0 else''))or i

You can drop the extra () which brings it down to 80.

  for i in range(1,101):print("Fizz"if i%3==0 else'')+("Buzz"if i%5==0 else'')or i

74

    for i in range(1,101):print(''if i%3 else'Fizz')+(''if i%5 else'Buzz')or i

70 now, still same idea.

    for x in range(1,101):print['','Fizz'][x%3==0]+['','Buzz'][x%5==0]or x

Excellent. Down to 68.

    for x in range(1,101):print['','Fizz'][x%3<1]+['','Buzz'][x%5<1]or x

My shortest Python solution is 59 characters. Two tricks, use while instead of range, and use string repetition instead of lists

  n=1
  while n<101:print'Fizz'*(n%3<1)+'Buzz'*(n%5<1)or n;n+=1

And here is a wacky one in 96 chars

  w=range(101)
  w[::3]=['Fizz']*34
  w[::5]=['Buzz']*21
  w[::15]=['FizzBuzz']*7
  for s in w[1:]:print s

You can save one more character with an exec loop

  n=1;exec"print'Fizz'*(n%3<1)+'Buzz'*(n%5<1)or n;n+=1;"*100

Nice, The 82 character one works for me also, on Mac OS X python 2.7.3

for i in range(1,101): print "FizzBuzz" if i % 15 == 0 else "Fizz" if i % 3 == 0 else "Buzz" if i % 5 == 0 else str(i)

derp, works better of course

Though I can't find out the score the page to test the code seems to be inaccessible if you are signed in. It just redirects you to the signed in page and the signout link is broken. Still it's a fun and cool idea

for i in range(1,101):print i%15==0 and 'FizzBuzz' or i%3==0 and 'Fizz' or i%5==0 and 'Buzz' or i has a score of 102

Redirects issue fixed. Can you try it now?

Works to login having trouble submitting however now

117 is my best Python solution yet, but I'm struggling to get higher than that!

nvm it's just running realllllly slow...