> and you can usually do a better job just by looking at server logs
Yes, if you only want to count visits and don't have a problem having all bot traffic included. For everything a bit more advanced you need a proper analytics tool.
Filtering out bot traffic is easy enough with server logs. A self-hosted JavaScript analytics tool gives you more data, but Google Analytics filters out Firefox users too; contrary to ReCAPTCHA's apparent beliefs, Firefox users are mostly not bots.
