Usually, people have a pretty good idea as to who is going to be visiting their sites. For me, it's generally friends from the industry or people who are using Google to try to find answers to problems. I get a few links from other blogs, but not many. Regardless, it's interesting to look at the host logs to find out who was visiting you.
For example, yesterday, my site was visited from someone at Halliburton.com. I'm not the most political blogger, and my government affiliation is city government only, so sorry, no multi-billion dollar reconstruction contracts here. I was also visited by a crawler from Marketscore.com. I can't find out what they do because my spyware blocker keeps me from going to the site. That alone tells me enough.
Back in October, my weirdest visits were from Google's proxy server (meaning someone inside Google was checking out my site) and Northgrum.com (evidently, I have a lot of information on electronic sensors and related systems hidden here without my knowledge).
So, what's the weirdest site you've ever seen in your host logs?