Helping people with computers... one answer at a time.
Web based email is handy but limited. Most do not allow direct access using a normal email program.
The answer not surprisingly is: it depends. But first, a quick definition.
POP3, which stands for "Post Office Protocol version 3", is the defacto standard for email retrieval by stand-alone email clients. When your email program, for example Outlook Express, downloads your email from your ISP, chances are it's using the POP3 protocol. Web based services skip this step because your email is never downloaded to a separate client. It's simply displayed via a web page you access.
Web based email has long been used as a way to check email while you're away from the computer. For example many ISPs offer a web interface to your email in addition to a POP3 interface. Even if your ISP does not offer such an interface, many of the independent web based email services such as Yahoo or Hotmail allow you to view your POP3 based email in their web interfaces.
But what if you have the reverse situation? You have all of your email in a Web-only service and would like to download it into a off-line mail client?
That's where the "it depends" comes in. And even then the news isn't really all that good.
With most services you are unfortunately out of luck. Most services, Yahoo included, do not have a separate interface to download email into an offline client.
In fact, Hotmail is the only web based service I'm aware of that supports a downloading client. And even then the only client it supports is Outlook Express. Periodically there are rumors that Hotmail will be dropping Outlook Express support but they have yet to pan out. And much like dropping support for Outlook Express completely, which Microsoft announced earlier this year and then reversed, this feature of Outlook Express is so popular that I'd expect a similar public backlash.
Note that Outlook (not Outlook Express - see here if that confuses you) claims support for Hotmail as well - however it simply amounts to viewing the Hotmail web page within Outlook and is not a true download. Microsoft has this article in the Knowledgebase that discusses how to set up this feature in Outlook.
Update: Since this article was published I've become aware of a couple of tools that can make Hotmail and Yahoo mail available via any pop3/smtp mail application. They require a little bit of configuration on your part and run as background processes on your machine, but they provide a layer that translates between the normal POP3 and SMTP protocols and the Hotmail or Yahoo web or proprietary interfaces. These said tools are Hotpop for Hotmail accounts and Yahoo Pops, an open source project for Yahoo mail. These are definitely not endorsed by Hotmail or Yahoo.
I've also become aware of the fact that while Outlook 2000 functions as described above, Outlook 2002/XP and Outlook 2003 do support Hotmail directly.