I created a test repository with a huge number of named branches — 10,001 to be exact: https://bitbucket.org/mg/10k/

When I go to the overview page and hover on the "branches" drop-down menu, then Chrome crashes on my system. Also, running
{{{
$ wget https://bitbucket.org/mg/10k/ O
-2011-12-05 11:22:34- https://bitbucket.org/mg/10k/\\
Resolving bitbucket.org (bitbucket.org)... 207.223.240.182, 207.223.240.181
Connecting to bitbucket.org (bitbucket.org)|207.223.240.182|:443... connected.
HTTP request sent, awaiting response...
}}}
seems to hang with no further output and no network traffic. That is strange since I can see the page in Chrome, but maybe you sniff the user agent?