Check your configuration a bit deeper. Your default Apache setup is probably installed as simply not allow traffic to /. For that matter, it's probably only configured to allow traffic to /var/www.
In addition to setting directory permissions (and as the dude above me said, you'll need at least execute on other to traverse the directory), you want to make sure that you have something like the following configured:
Options Indexes FollowSymLinks MultiViews
allow from all
If you follow the above solution and just create a symbolic link from /var/www back to your home directory, you'll need to make sure Apache has been told that it's okay to follow symbolic links, by adding
FollowSymLinks to the Options stanza for your existing document root.
Lastly, if you're using CGI under suExec, the symbolic link is your best bet as suExec has a compiled in "safe" path. There's an easy way around that if you're using a Debian distro, though.
Yet another approach would be to just define a new name based virtual host that points to your home directory.