I use a multitude of tools to measure site traffic, with Google Analytics and Woopra being two of them.
Generally speaking I'm not really concerned about privacy issues in the context of using these tools. But it's important to note that I represent one person (myself) and not an organization. That said, in an effort to be transparent to users what I've started doing with sites I look after is to make amendments to their Privacy Policy -- specifically stating that Google Analytics is being used on the site to collect information about visitors to the site. I go on to state in the privacy statement that when a visitor comes to the site, information is collected about them by these third-party tools for the purpose of traffic measurement and site optimization. I have a section in it called "Types of Information Collected" in which all this is described in some detail, including explanations for several key terms such as IP addresses, cookies, and so on.
Get to know the tool you're using and read up on its own privacy policy. You should understand common basic concepts such as "cookies" and "IP address", and how these things are used in the context of your tool.
If you're using Google Analytics or any other third-party web measurement tool for that matter, I believe that as an organization you need to familiarize yourself on how the provider is collecting and using your site's traffic data. Moreover, you want to make it clear to your visitors via your privacy statement that you're making use of a third-party provider to collect information about their visits.
Smart to have a privacy policy if you don't have one already.
Yann