i have tried a couple...
the most exact conts i get from shinystat,
www.shinystat.it and i guess
www.shinystat.com as well. under 1000 clicks = you can choose the free alternative ...
terra has one counter as well.
http://www1.terra.com.ar/servicios/
if you scale the image to 1 pix x 1 pix it stays unseen.
a third i have tried i got from
http://webtools.html.it
that's just a script = not seen unless you look the source.
the statistics ae never the same. supposing you try 3 stats on the SAME page you get probavly 3 different stats.
shiny is quite nice and you get a lot of info, but it stays public in unpaid versions. those others you can hide. but they are not as exact.
how much info do you want? how you were clicked etc? OS? browser? screen? or plain click numbers?