I don't think people can see your searches. I've never heard of that or seen anyone searching for me (or heard my DH or friends say anyone has searched for them). Also if you have specific people you don't want to find you, you can block them from seeing you in any capacity on Facebook. You can also change your security settings so only certain people can find you at all.
In general, the only people who can see your profile are people you approve as your friends. However, if you join a network (like your company, or city), the default is that all of the other people in the network can see your profile. I don't think most people know that! I think you can change that in your privacy settings; I'm not in a network for that reason. Also you have separate settings for your photos where you can allow various people to access (only specific people you list, friends only, friends of friends, everyone). When other people tag you in a photo, you can decide who gets to see that as well. I think the security is pretty good. The only annoying thing is that the defaults are pretty open, so you have to change things if you want tighter security settings.
There is definitely no way to see who has searched for/viewed you on facebook, and they don't intend on making it that way. I read something a while back that the people who run facebook don't want it to become like an internet dating site, and that's part of the reason they don't have that feature. I know there are outside sources on Myspace that say they will tell you who has been looking at you, but I've also heard they are very inaccurate. I haven't heard of any outside sources providing any service like that for facebook yet. I kind of appreciate the privacy, although it can make it really difficult to know if you are finding the right friend when they have a common name!
The various privacy functions are very helpful, as long as you remember to go back and change them to your liking. Like most other networking sites, the default is so that everyone can see your "stuff," but you can change them to however you like. I've got most everything set to "friends only," but if an album involves DH or other people I know from Facebook that arent on my f-list I might change it to "friends and friends-of-friends."
The day the free milk paid off -- November 11, 2006.
When you are in your profile - on the right side, there will be a message that says "your profile has been viewed X times in X days or your profile came up in X searches". You click the hyperlink and you can see who viewed your profile. However, in your settings, you can block this function.