Windows Live Alerts help you keep up with forum replies, stocks, traffic, sports, and a quite a few other services. As you might imagine, when something changes in the source, you can be notified via email, IM, or phone. I don't have any complaints about the service, but I would like to suggest one addition: search-based alerts. Once again, this is something Google offers that I thought was pretty nice. Essentially, you'd sign up for an alert and would receive an email daily, weekly, or monthly with whatever new search results are added to the global search index.
Some might wonder how/why this is useful. Well, there were a few instances where I used it. First, I put my name in there. Initially, this was just to try out the service to see what it was like, but after a while, I found it helpful to see how/where references to me came up around the web. Some I knew about, but others I didn't. This allowed me to respond to someone's blog if they were commenting on something I said, for instance. The second use was to get alerts on a few of my favorite tools. At the time, Update Version (command-line .NET assembly version updater) and DotNetNuke (open source .NET portal) were two examples.
The concept is pretty simple. I don't know what it'd take to build that into Live Search, but it would definitely be a nice-to-have.