Counting your syndication feed readers
Suppose that your blog has a syndication feed, and you would like to know how many people are reading it. While you could just look at your web stats to see how many different people pull your feed, the numbers aren't you'll get won't be too useful. Some of those feed requests are from aggregators and not all aggregators report readership numbers to you (and some of them have no idea, for example planet-style aggregators that just put the result up on a web page), plus not everyone who pulls your feed is still actually reading your entries; you have to assume that a certain amount of feed subscriptions are just quietly rotting away unread.
(These effects compound, of course. I have no idea if Google Reader's reported numbers exclude people who are subscribed but not reading, for example.)
I will cut to the chase: the hack solution to this is images. You can crudely track actual entry readership by putting a (unique) image in your entry, one that you host, and then counting requests for it in your own logs. Of course this works best if you already write the sort of blog where you include images in your entries, either as part of them or simply for visual flavour and design. Otherwise people may start to wonder why your entries periodically include random images.
(There are all sorts of issues with this which make it only a crude measure. Carefully making the image uncacheable by proxies and serving cookies with it will help with some of them.)
There are at least three sorts of images you can use for this; little invisible 'web bug' images, more or less unimportant images that are just used to add visual appeal and design to entries, or images that are actual relevant parts of your entries. Setting aside the issue of being nice to your readers, the last choice is the pragmatically best one. If the images are actually an integral part of your entries your readers will make sure that they see them even in the face of feed reader issues (going so far as to visit your entry directly if necessary). Less important images can drop out without the readers caring (or even noticing), so you will undercount such people.
(Web bugs are especially likely to get screened out, of course. I wouldn't be surprised if some feed readers and aggregators do it automatically by now.)
PS: I'm sure this is well known in the part of the web world that cares about readership stats. I just feel like writing it down here for the record.