Two absolutely must-have blogging analytics are Google Analytics and FeedBurner. FeedBurner lets you know how many RSS subscribers you have, and Google Analytics gives you a bunch of awesome stats about your website in general. For example, you can know the keywords by which readers reached you via organic search, the amount of time readers spend on your site, unique visitor counts, hit counts, etc. Google Analytics is super easy to install, so there’s really no reason not to have it.
FeedBurner is also super easy to setup, but there are a few use cases that require some technical fiddling:
What if you need to change your feed URL in the future and you’re using FeedBurner’s URL?
When you sign up with FeedBurner, they’ll give you a feed of the form feeds.feedburner.com/some_feed_name. If you link your users to this feed, then you’ve lost all control over the whereabouts of your feed. Users will start adding that feed to their readers, and you won’t be able to redirect them if necessary. FeedBurner offers a service called MyBrand that allows you to create your own host (e.g. feeds.example.com) with a CNAME record such that users will subscribe to feeds.example.com/some_feed_name and will actually be reading from feeds.feedburner.com/some_feed_name. This means that you have control over the whereabouts of your feed. FeedBurner has a very nice tutorial on how to set this up.
If you already have a bunch of subscribers, then how will they be redirected to a FeedBurner feed?
You can make an Apache Rewrite rule that forwards your old feed URL (probably example.com/feed) to the new FeedBurner URL unless the user agent is FeedBurner. Take a look at this post for more info.
Here’s a little diagram I whipped up to describe what happens when you’re running MyBrand and Apache rewrites:

Again, Google Analytics is cake to setup. FeedBurner by itself is also cake, but the two cases mentioned above do require some fiddling. Go install both of these if you haven’t already!