Why I'm switching to Gmail
I've been using Yahoo! Mail for several years, and it's been great, but Google is doing more to advance technology (especially in some areas of interest to me), and I'm finding myself compelled to switch to Gmail, because I think it's a more "intelligent" email application.
Labels (also referred to as "tags" by Flickr, Technorati & del.icio.us -- here's a good intro to tags and why they're useful), are probably the main specific reason I'm switching. Tags free me from the typical contraints of folders (though folders as a concept are still useful!) and enable me to put messages in more than one category. I don't mind folders being the metaphor for looking for things in those categories, but I've always resented the fact that folders (as implemented in most contexts) limit me to a single category.
Notably, blogharbor.com, where I host my blog, takes the same approach, letting users put articles in one or more Categories, something the very popular (and Google-owned) blogger.com does not, AFAIK. This is one of the reasons I chose to host my blog at blogharbor.com.
Google describes labels as part of their approach to creating "A more flexible filing system", something about which I plan to write some day.
More manageable Inbox
It takes a while to get used to it and start seeing the benefits, but Gmail provides a much more manageable Inbox than many other email clients (web based or not!).
"Conversation View" keeps your conversations together - Gmail groups messages related to a certain topic (or "thread") together to create a "Conversation View":
I don't understand why people accept the idea of using a Sent folder (I have an article about this planned too!) in email. Saving messages in Sent causes your conversation to become fragmented; the part you write is in one folder - Sent - and the part others write is in your Inbox or whatever folder you file it.
It's still useful to be able to view all the messages you've sent (a capability Gmail provides), but that does not have to mean they are filed in a different place.
If you're not using Gmail, the way to get around using a Sent folder is to Bcc (blind carbon-copy) yourself on each message you send. Unfortunately, Yahoo! Mail (which I'll refer to a lot not to single it out, but because I use it a lot) doesn't provide this capability (why??), so for my personal mail, I'm stuck with a Sent folder. For my work mail though, I do have the option to Bcc myself, and I haven't used a Sent folder for years. That means if I look for email about project X, I find everything everyone involved in the conversation said, in a single place. With Gmail, you don't have to Bcc yourself on everything, because it already groups what you write with what others write on the same topic/thread.
Less cluttered list of messages - Conversation view provides a very efficient use of space when displaying a list of messages. I currently have 9 conversation threads in my Gmail Inbox, with a total of 31 messages. With Yahoo Mail (and many others), the 31 messages would all be displayed "flat" (each message displayed in a list) and unrelated in my Inbox, as opposed to condensed into just 9 conversation threads.
Keep track of where you are - Also of note, when you look at your Inbox in Gmail, there is a > to the left of the thread you last viewed. This is much more useful than you might guess, when switching between reading messages and the list of threads in your Inbox!
I know threading isn't new, but I think Gmail does a nice job of presenting a user inteface that takes advantage of it. This really helps with managing mail, but you'll probably get a better sense of this after working with it for a while.
Better & faster management of Drafts
Gmail makes saving a draft quick & easy, and unlike Yahoo mail, once you create a draft, future saves are updates to that same message; Yahoo Mail creates several copies, each is a later revision with the most current updates. I'm sure that works for some people, but I don't care for it.
Update: Gmail now auto-saves drafts!
Better (indexed!) searching
Google applied the idea of indexing (building a list of keywords and relating it to content) web content to email.
Indexing is effectively doing the "work" of searching in advance (and updating it regularly), so the search takes a lot less time when you request it. When you search your Gmail, you get results very quickly because the server simply looks in its index for the search term, and shows you the messages that contain it.
Try doing a search in your Yahoo! Mail and compare it to a search over a similar amount of data in Gmail. Disclaimer: I can't yet actually do this myself (I only just started using Gmail), but I'd bet you a dollar the Gmail search is faster.
Some people argue that we shouldn't bother to put things in folders since searching is so good these days, but folders have long been a metaphor for manual categorization, a capability that's extremely valuable. We should start getting into the habit of using labels (or tags, or keywords) instead of physically moving data into folders. More on this in another article.
These are my thoughts on the matter so far (March 2005); I will likely add more reasons for migrating as the occur to me...
Since writing this article, I've found a wealth of information about Gmail over at gmailtips.com.