i use both SiteMeter AND the AXS script, and a third script CGI script (just a basic multipage text-counter).

sitemeter for my 'index.html' page,
the CGI text-counter for all other pages,
and the AXS on all pages and links.

here is more information on the AXS script:
http://www.xav.com/scripts/axs/full.html

they log the following:

Web Browser (Netscape 3.01 Gold)
Abbreviated Browser (Netscape 3.X)
Operating System (Windows 98)
Visitors Top Level Domains (.com)
First Level Domains (xav.com)
Full Server Address (noc.xav.com)
Visitor IP Address (206.134.243.3)
Hits from Other Sites (Full URL)
Hits from Other Sites (Domain Only)
Hyperlinks Followed From This Site
Hits to Local Documents
Average Number of Hits Per Visitor
Hits By Day of Year
Hits By Day of the Week
Hits By Hour of the Day

it can easily be configured to NOT log hits by your IP address.
you can find your IP here: http://www.simflex.com/ip.htm