A "Servlet Container" profile (potentially without JSP) and a "Web Application" profile (containing JSP, JSF, and WebBeans) both might be appropriate.

Not meaning to flame, but my team will probably not use them. To me, the whole profiles bit seems to be aimed more at container vendors, and what they have to support by default. When we want make web applications, we simply download Spring + a JPA provider and then add in jars as necessary. Sure, if a profile means we have those jars already, great, but it's very easy to download jars and stick them in your classpath. I'd much rather just go get them and have control over the process, than having a bunch of stuff I'll never use (JSF) forced on to me, although as long as they don't conflict with my project's libraries then I could care less.

When people say they're not interested in Java EE profiles, do they mean they don't care about Java EE, or that they don't care about the profiles part?

The full profile should include JSR-286 (Portlet 2.0), which has recently been submitted to the JCP for approval.