I had a strange problem on Ubuntu 10.04, the AWStats cronjob was not working even though everthing worked fine on the command line as root. The solution was to add /usr/bin/perl in front of /usr/lib/cgi-bin/awstats.pl. So here is the working cronjob, hope it helps.
*/10 * * * * /usr/bin/perl /usr/lib/cgi-bin/awstats.pl --config=www.example.com -update
(replace www.example.com with the part of the configuration file name, here it would be awstats.www.example.com.conf)