I created a Google Alert to find out when anything new is said about one of my favorite authors. I'll have to wait until tomorrow to see how it works. I can see how this could be useful for many topics. One problem with using this with my students is that many of them do not have email accounts and we actively discourage students from checking their emails at school.
My email is gmail and I use it extensively. I just wish it would let me sort messages. I get emails from mailing lists. Each email is numbered. I would like to be able to read them in order from the top of the list down but have to read them from the bottom up. This is really just a minor annoyance. I love the ability to set up filters and to label ane keep messages in folders.
I also keep my personal and work calendars on Google Calendar. I have heard of some teachers who use Google calendars for their lesson plans. I haven't gotten that detailed and don't plan to either. I have my Google Calendar as a widget on my iGoogle home page. It is very useful as I space out on what I'm doing and where I'm going rather frequently.
From the For the Curious section, I use the downloadable Google Toolbar on the computers in the Elementary computer lab. I like the convenience of it when working with students. We frequently use the drop down menu to get to images when we are searching for pictures. Third and fourth graders do this to find pictures to illustrate projects for me.