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The thing to look out for is that sometimes the "free" stats counters imbed hidden links within the counter code, so you end up giving a link from every page of your site to some spammy diet pill or Viagra site.
[edited by: Jane_Doe at 4:21 am (utc) on Feb. 19, 2007]
As an aside, some stat counters use a cookie. This can cause problems where someone visits your site using their company server which sees a third party cookie. I don't know the details but I think a few company servers are set up to prevent their employees visiting sites that have third party cookies for some sort of security reason. Not common but another potential problem.
.... and another problem is stats that use an image to count the visits. The counter won't work until the image has been loaded by the user. This makes it very unreliable and can cause page loading problems for the user.