You probably didn't even know Google had a web history feature. And it seems to be active for some people and not for others; in the couple of articles I've read so far, nobody seems to know what the criteria are. (Has it always been opt-in? Has it changed?) But if it is on, the the service is tracking all searches you make (and optionally, which results you click on) while you're logged into your Google account. For many people, that's a good percentage of the time they use their browser.
Now, before you start thinking Google is some crazy company keeping your data for who-knows-what, you do get something out of it. For one, you can go back and see what you searched for on any day in the past, which is actually a pretty cool way to look back, and on occasion it can help you remember what you were doing on a given day, if you need to figure it out. Also, if you know you've successfully searched for something in the past, but now don't know what search terms you use and can't find it anymore, you can probably figure out what your search terms were from the web history. Additionally, if you've enabled the more-powerful tracking options (these are opt-in), when you run a search you'll see text underneath any results you've clicked on before, with the date you last accessed them through a search. This is really handy, because if you've been to a site before it makes it significantly more likely that you'll be looking for it again. Google can also use the information to give you (supposedly) more relevant results.
Of course, having a history of all the searches you've ever performed might be unattractive to some. If that's you, feel free to clear it out. But keep in mind that this won't necessarily prevent Google from collecting some of this information about you anyway (see #2 on this CNET article). Especially with that in mind, I find that for me the benefits are worth the potential privacy risk. Personally, I never clear my history in either Google or my own browser, because I frequently want to go back and search where I was a couple of days ago. Someday this is probably going to come back and bite me when someone steals my browsing history, but that won't be that big of a catastrophe, and I'm willing to take the risk for the convenience.
For the most part, I trust Google to keep my information. Someone has to deal with my email (okay, technically I could run my own mail server, but that's not really practical for most people). In my opinion it might as well be Google. Some people decry the fact that Google "reads your email"—a computer scans the content of your messages to determine advertisements that might be related. That doesn't, however, mean that anyone at Google is actually going to read the words in your email and get any meaning out of it, nor does it really scare me. There are plenty of much easier ways for someone to intercept the content of my email over the Internet, and I highly doubt that keeping an archive of the entire world's email is one of Google's goals. And in general, I trust Google enough to keep my information. I wouldn't trust a random start-up company with my history or my email, nor would I trust Facebook. And in exchange for everything that Google offers me (search, email, YouTube, this blog, . . .), I'm perfectly willing to let them display targeted advertisements.