POP3 for me. I've got things set up so that mail gets downloaded onto the desktop and onto the laptop, so I never have the problem of mail being in the wrong place.
Back in the old days, when using one's laptop on the road wasn't as easy as it is now, I used to forward mail to a Hotmail account when I was travelling... then I discovered mailreader.com and started using that in conjunction with my POP3 account... but now that I can more or less hook up my laptop to the Internet everywhere I go I just use Thunderbird for everything. I don't like webmail.
There now seems to be a new generation of Internet users who don't even seem to know what a mail client is, and who can't figure out how I manage to read and compose replies to emails when I'm half-way across the Atlantic...