How do I limit size of a file to 1 MB or something like that under Linux?
Check out the man page for limit or ulimit. You can set this in /etc/default/login for all users.
The file is on my webserver and users can add stuff into it, and I need to limit the size. I don't have that much access to system.
What webserver are you using (and version)? Do you have admin rights to change the webserver configuration files?
Apache, and I don't have admin rights, although I can ssh into the server.