It's funny you should mention
www.statcounter.com Strat... I found them after doing a quick Google search and have been *blown away* by what I've seen (I, like most, remember third party counter/source solutions to be poor quality, shady hacks that force adversiting on you).
(Incidentally neumannu47 the sites free service is perfect for what you are looking for, as you can specify either a visitor or hit counter with a wide range of nice clean counters with customizable colours).
But far more interesting than the (robust) counter solutions is the amazing detailed user analysis and summaries that Statcounter does on your visitors. They have an excellent geo-targetting databank that they cross reference with your logs so you can view your visitors by country (often down to what *city* they're in) as well as the exact path through your site they take... (ie: A user from Manchester England followed an external link to this page, then went to this page, then went to this page).
This is all intigrated with summaries by country, by browser, by os, even what screen resolution they are using. The drill down is not quite fully implemented yet, but what has been is quite brilliant and allows you to make some very intuative leaps about your users.
They also seems to support W3C and xhtml complient versions of their tracking code which is very welcome.
Anyway, I only set up with them this morning - but it seems (in my limited experience so far) to be a very quality product that has made me *far* more excited about my stats than I normally am. Depending on how this test rolls out I'll be adding all my sites (did I mention multiple sites and users under one account?) I will gladly pay for their "extended" service (allows a greater visitor cache, free service logs the past 100 visitors) given the quality of the product I've seen so far.
Certainly made my morning, now I'm going back to refreshing my logs every five seconds </gush>