It's generally considered to be the case that under the GPL providing a webservice based on opensource software does not constitute "distribution". This is why the AGPL exists - under the AGPL using software to provide a service does constitute distribution and thus requires you to provide the source code of software which links to AGPL-covered code to the users of your site.

Any data that you create entirely yourself from scratch and serve using a lamp server is not bound by license and you get to decide the license(s) you want to use to distribute your data. You can use different licenses for different parts of the site.
[url]http://creativecommons.org/[/url]
is a great resource if you want to redistribute some of your own work under a license.

Most people license their entire site's content under one license but some use a different license for certain content.
You can see at the footer of this page that the Linux foundation have chosen the proprietry Copyright ©. Which means no one is authorised to do anything with the content without permission.
(Which is a little misinformed for a community website.)

GPL v2 it's just one kind of license you can use to distribute web services, it's not the only one as you see from other comments.
This license for example allows you to modify code and distribute your work as GPLv2 as well, users may require source code from you except when you're using applications for providing web services to others (software as a service in general). Look at Google... :-)