In my humble opinion, Google Analytics is one of the (or maybe the) best free webstatistics programs. Nevertheless I would like to point out that there are plenty of opportunities to improve the user interface using the data already available.

1. Monthly and weekly stats: It would be a lot easier if you could select weeks or months as timescale. It would improve the possibilities to spot monthly and weekly trends and could eliminate the daily fluctuations.
2. Trend lines: Many number crunching aps have this available. A line running through your diagram could show (for example) the 30-day average and the 10 day average. It not only enables you to visualize the trend (going up or down) but also gives an idea about the speed in which this happens (10 day average tops the 30 day average).
3. More selection criteria in columns: It is possible to to sort tables. This could however be improved by features like eliminating the 100% bounce rate pages that only have 1 pageview or by sorting data by multiple columns, such as highest bounce rates of top content.
4. Long tail graph. Rand of Seomoz came up with a post on a statistics program enabling you to visualize the longtail of keywords. I would like to do this in Google Analytics.
5. Directly change the date range: Most of the times I start analyzing my monthly numbers. Sometimes I note a sudden increase in for example the referring sites. I would like to be able to look at the figures of that day by only clicking the dot in the graph. Currently, hovering or clicking this dot shows an alert box with minimal information
6. Spice up the site overlay: If you are familiar with crazyegg.com you know what I mean. They have a heatmap showing the visitor clicks on a page. By increasing size, color and intensity of the area on which visitors clicked you can instantly see what attracts visitors. Moreover, they also show clicks on areas that are not hyperlinks. It shows if visitors are somehow confused on where to click. Very useful information.
7. Compare sources: You should be able to put multiple sources in a graph. For example, this enable you to compare paid and non-paid visitors. Or to compare multiple referring sites into one graph. Is it a seasonal drop or limited to one source only?
8. Include Feedburner data: Both Feedburner and Analytics are owned by Google. Why not include the Feedburner data into Google Analytics?
9. Custom tags: I would live to give my comments to spikes or drops in the graphs by adding markers with comments. You could mention that the spike originates from Digg or for example take up changes you made in the design. Ideashowever has a very interesting post in this respect.
10. Include Adsense data: On the wishlist of many people but probably on the secrecy list of Google.

If you know of features I forgot, please leave a comment so that I can extend this list.

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