I came across Funambol. It is an open-source application, specifically written as a mobile synchronisation solution. There is a download for your own server (presumably for corporates who need their own push email services like Blackberry, but without wanting to pay RIM for the privilege) but here is their sample demonstration portal, free-to-use for smartphone owners who want to keep their calendar, contact list and emails safe online.

I wondered if it would be able to synchronise with my Thunderbird & Lightning (that sounds corny) email and calendaring application. Calendar ... YES. Contact list ... YES. Email ... NO. Hmm, ok, how to get emails synchronised? It supports Gmail directly! Coolness!

Sidenote: to have multiple devices synchronising with gmail, you need to alter your email address slightly. You need to prepend "recent:" to your gmail address "recent:username@gmail.com", to ensure that all your sync clients can receive the email, rather than just the first client to connect.
EDIT after looking at my Funambol entry for linking to gmail, and seeing that it's IMAP, I went to gmail help, and it explained, step-by-step, how to use IMAP for Thunderbird, instead of POP (hint: ignore Thunderbird's email account set up wizard). Much nicer, having everything to do with my email properly synchronised.

So now my calendar and address book are synchronised between my phone and my laptop, and my emails are synchronised between my gmail and my phone! Excellent! And with little hassle, too!

There are still some limitations. For example, I've started to use Google Calendar, so my personal appointments can be stored online, and viewed/edited by those to whom I give permission. Funambol doesn't support Google Calendar, so I have to duplicate calendar records inside Lightning to get my appointments to synchronise. I hope this will soon change, as Google has just introduced CalDAV support for Google Calendar; so when they've ironed-out the bugs, I hope Funambol will synchronise with it.

But, all-in-all, it's like having corporate managed mobile services, provided free by an open-source application. I am already having better experiences with this than with more than 10 years of supposedly integrated messaging while working at some of the world's largest IT companies!

I'm using Windows, because it works for me and I like it.
I'm using IE, because it works for me and I like it.
I'm using Gmail (and Google Calendar), because it works for me and I like it.
I'm using Thunderbird (with Lightning) because it works for me and I like it.
I'm using Funambol, because it works for me and I like it.
I'm using Pidgin, because it works for me and I like it.
There are other applications that work, but I don't like as much (eg: Firefox). There are other applications that I like, but don't work for me (eg: Linux). But this is my list of critical applications that I think I'll be using for the foreseeable future. Other applications may come and go (for example, I'm currently using OpenOffice, but thinking of migrating to something like Google Docs for collaboration features and automatic backups), but I think my ideal core set of applications has finally been defined, for the first time since I started working on computers, 21 years ago.