There are so many different webmail services on the internet, from the huge ones like Yahoo, Gmail, Hotmail, to the much smaller ones from private websites and ISPs. There is a lot to worry about with e-mail these days but some of these front line webmail services are really a great way of helping to protect your system.
Location and Applications
Two of the biggest benefits of using web based e-mail as your primary e-mail service is the fact that you can essentially use it from anywhere with any application. As long as you have an internet connection and a web browser you are probably good to go. Of course some organizations block certain websites (to keep people doing their jobs at work) you might find yourself unable to check your e-mail at work. But if you are on vacation or at home, or at a hotel on business then you should have no trouble getting at your e-mail.
Spam, Phishing, Worms, and Viruses
This is probably the single biggest reason you should consider switching to a webmail interface for your e-mail. Most good services screen or filter your e-mail to help keep you safe by deleting or quarantining dangerous, or potentially dangerous e-mails. G-Mail for instance has a really great spam blocker, will not open pictures or links be default unless you tell it to, and recognizes e-mails with possibly forged headers and warns you that the e-mail or sender my be fraudulent!
By using web based e-mail you also have the ability to have all your history of e-mails or important documents follow you wherever you roam. This is even more true recently since all the major providers of webmail are drastically increasing your storage capacity. Why bother deleting your e-mail when you can archive it and then pull it up later when you require it, possibly from the other side of the world, or on a beach in Mexico. If you do all your e-mail from one computer and store it in offline media then you are heavily restricted when you are away from home, unless you have someone to mail stuff to you upon request.
POP3 / SMTP
Most webmail services now offer you the ability to use your normal e-mail program at your computer if you don't want to always go to the web to download your mail. I personally prefer the web based method because it's one less program cluttering up my computer and with broadband internet access it's just as quick as being on my computer anyway.
A lot of the bigger web based e-mail providers have applications that run in your task bar or system tray that will notify you when new e-mails arrive. This can be setup to check every few minutes or almost in real time. G-mail for instances gives you the "G-Mail notifier" which is a great little tool! Other e-mail servers are integrated in to various instant messenger applications such as ICQ and MSN Messenger.