Other things, such as mkdir, are affected by the umask:

andy@okura:[/tmp/test] mkdir foobar
andy@okura:[/tmp/test] ls -l
total 4
drwxr-xr-x    2 andy     andy         4096 Jun 20 14:55 foobar
andy@okura:[/tmp/test] perl -e 'umask(0666); chmod(0777,'foobar'); \
> mkdir('foobar2',0777);'
andy@okura:[/tmp/test] ls -l
total 8
drwxrwxrwx    2 andy     andy         4096 Jun 20 14:55 foobar
d--x--x--x    2 andy     andy         4096 Jun 20 14:55 foobar2
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