Ok, so we all want to measure traffic "correctly". But, we also want to have 'good stats' for our clients. Through my research, I've found some interesting facts on stats:
The good: More accurate stats and, in some cases, are free (i.e. sitemeter.com offers a great system).
The bad: Doesn't count all statistics (like web bots and other miscellaneous incoming traffic) & uses a third-party's collection of statistical data (i.e. they can use your data for other things)
Server-side - Installation of a statistics system on your server. The software then analyses your log entries and disseminates the data for your viewing pleasure.
The good: Counts everything. Great for showing 'more traffic' for your web clients.
The bad: Counts everything...not as accurate. Plus, if you own the server, you've got more responsibility to deal with. Lastly, server stats (really good ones) can get quite expensive.