Google Analytics is a major website traffic analysis suite, based on the Urchin on Demand from Urchin Software (bought by Google in 2005). Unlike the Urchin product, Google Analytics is hosted by Google, so bloggers who are using services like Blogger can use Google Analytics. The downside is that unlike a solution that is hosted on the same server as your blog, Google Analytics cannot process historical log files. That means when you install it, it will take some time for useful data to accumulate.
Getting on to Google Analytics might be a problem. When the product was rolled out in November 2005, the intense demand for accounts forced Google to back off from the free-on-demand approach. Google Analytics is still free, but when you apply, your application gets approved by lottery.
I have read that it can take upwards to two to four weeks to be approved.
Now this is important -- I don't know that this is even true anymore. I applied and was immediately approved. In fact, I was suspicious, and thought I was looking at some sort of tease page telling me what I would be enjoying once I was approved, but it was the actual Analytics members page.
So it may be that the lottery is no longer in operation.
In any case, Google Analytics performs many of the same operations as Sitemeter.
When you first get to the members page, you see a "dashboard":

Nice at-a-glance view of activity. Basic traffic data, how many visitors are new or returning, where they are coming from (web referrals and geographically). There are a lot of on-screen controls to change date ranges, export the data in many different formats, change the detail level of the labeling, and so forth.
Drilling down, you can view your traffic by any date range your find convenient (including going back into the past as far as you care to go, to any level of detail):

Here is an interesting metric you don't get with Sitemeter -- your "bounce" rate. How often do people come to your site, then immediately leave? Is there a particular page that is notable because of a high rate of bouncing? Now you have an idea of what pages are drawing in visitors and which ones are driving them away:
This is cute -- the Site Overlay. Google creates an image of your site and overlays traffic pattern data so you can see where users are clicking and where they are not:
Not all of this might be useful to every blog. For instance, there is tight integration to Google AdWords, but I doubt many bloggers are using AdWords. Similarly, if you are buying ad space on other websites to promote your blog, such as with a banner, you can create tagged URLs so that when someone clicks on that banner, Google Analytics will know that someone reached your site via that specific banner, giving you the metrics you need to see how effective that banner really is. But then how many bloggers advertise?
Maybe with Google Analytics, some might decide to try.
But even if you only use 20% of what Google Analytics has to offer, you'll be impressed by its functionality and its slick presentation. Check it out and see if it offers you something you've thought was missing from your current tracking system.