I'd like to send an email with a hit counter in it (invisible), which counts how many people open it. Ideally, I'd like to count both total hits and unique visits, but for now either one will be satisfactory.
The simplest is to put a 1x1 transparent GIF in the email and count your logs will show how many times its downloaded. This would not be too accurate for total hits, because of caching, but should be a good ballpark for the uniques.
The more difficult one requires a CGI script to get called and up your count. Most simple, free CGI counters would work, I guess.