Wait, did you say "short and fast and Perl"? One-liner, then?

$ time perl -MPDL -e 'print transpose pdl long hist +(10*random 1e7),0
+,10,1'

[
 [      0  998557]
 [      1  998651]
 [      2 1000878]
 [      3 1001181]
 [      4 1000788]
 [      5 1000577]
 [      6 1000108]
 [      7  999979]
 [      8  997430]
 [      9 1001851]
]

real    0m0.290s
user    0m0.215s
sys    0m0.074s
[download]

Well, twice as slow as kschwab's code, but isn't he a cheater: you asked to "generate 10 million random integers", and only then "count the occurrence of each". If you ask where are integers above -- bin centers effectively "floor" random numbers in each bin, to bin's lower limit.

P.S. Generating explicit integers as

is only very slightly longer (in both length and time).