As everybody else, I'd like to give my 2 cts on the current mail/thunderbird discussion, and I'll do it cent-wise. I'll start off with mail.
Mail matters. As of today, your email address is the root cert for vast majority of your online identities.
POP/IMAP matters. Your emails are a valuable asset, and open and interoperable protocols (read, APIs) guarantee users power and choice over what to do with that data.
Email accounts matter. ISPs used to lock in their customers via their browser/connection software. Today, ISPs lock in their customers via email accounts. This is a real competitive advantage by raising the barrier to switch ISPs and thus leading to less competition between ISPs.
Sadly, email software matters. Todays email traffic has a malicious-content problem, so your email software has to be "safe", no matter where it runs.
Webmail does not matter. But webmail is vendor lock-in par excellence, and it does not give the user power of her or his data. It's nifty that you can access your mail through a browser, but in terms of empowerement, it doesn't matter.
Email is a unique high-value asset of human being on the internet, with a particular impact on security and choice, and thus, IMHO, has an outstanding role with respect to the Mozilla mission and the manifesto. It's not outweighing the web, but one without the other is vastly less valuable. Something that I wouldn't say about calendaring or VOIP.
I'll do a Thunderbird-specific piece shortly.