It is obviously possible to run a site without access to Perl and/ or PHP by using the counters, forms and mailing lists; polls, search engines and so on provided by free hosting services. If, however, the intent is to do as much as possible yourself - and with as little as host imposed advertising as possible - then Perl and/ or PHP access will be required.
Just checking whether a host does provide this access is, however, not enough. Some environments these scripts are run under can be extremely restrictive, ultimately leaving the scripts of little to no use. When using PHP scripts, for example, it is vital to ensure that the host does actually allow the mail function to be used, as it will otherwise not be possible for the script to send e-mail.
In a similar way, if the user has no access to 'sendmail' - which is a computer program for Perl script users - or a similar programme, he/ she will again not be able to send mail.
In short, when looking for a free hosting service, it is essential to not only check for bandwidth and disk-space allowances, but also whether Perl/ PHP access is provided to the extent required to perform all the functions you desire for your Website.