The images I've included below show the breakdown by country of visitors to my blog over the course of last week, then the second one lists in more detail every country that views have come from. you can narrow this down to city as well. Other useful things you can check are which pages are the most popular, which websites people are directed to your site from, how long they stay (this can sometimes be a bit painful), and lots of other useful, or useless, information depending on your point of view/general inclination to nosiness.
What I found most useful was information on how people had found my blog - what terms they had searched for or what website they had come from. This made me think more about the tagging I use on my posts and I have resolved to try and be a bit more thorough in my tagging - treating it more like my actual cataloguing work than I have done in the past.
I haven't started using it yet for the WFSA Flickr account for two reasons, the first being I thought I would try it first with my Flickr account to see if it worked. With StatCounter, and I assume it is similar whatever software you use, you have to input the HTML code in to your profile on Flickr then add the web pages to your statistic software account. I'm find doing this with my own account but I was a bit unsure with the work one - does this give them access to other information on your Flickr account, do they have rights over the statistical data as it is displayed on their account? These questions are things I would rather investigate more fully before using it for workplace statistics - but for now I'll keep enjoying using it for my own web pages.