I myself take a look on them ... but my indicator is how many sales I make.
Sure you can not see what is working without statistics ... but to much...
I also must admit that I lost focus watching to much statistics ( how many are visiting my site rather then going for the sales ).
How about you?

There are some thing in site log that must be take in mind.
•   Observe at the Apache-logfiles, you can check here the number of users.
•   You can notify how visitors move about your website because of caching at the client-side.
•   You may not at all know how your visitors arrived at your website because Referrer-information may be incorrect, or missing.

The main purpose of analyzing the statistics of a website is to look for any new or effective trends and also to research the rank of your marketing campaign success. Although statistics can be misleading at times, (for example, a person who visits your site may not have necessarily read it fully and so cannot be considered as a hit) but it does give a very good overall estimation of your website.

Rather than looking at numbers, analyzing the trends is more important. Web statistics are important because it helps you to understand the quality of visitors or the performance of your website or pages.

your statictics helps you in changing your marketing stretagies, regarding your websites services.

In my opinion site statistics is still important because you can watch your SEO and maintain your likelihood of being found in the internet. Sales Conversion is also important because you can work on your sales pitch and determine what really works best.

I use my site statistics for analyzing my SEO work.

Getting traffic is not enough,we need to ensure that traffic converts to sales.Google analytics gives indepth insight into your traffic,actual page views..etc,these information can be used to tweak the site for optimum result.

Site stats are very important and surely frequency of how often to check depends on your marketing campaigns.

As you mentioned stats related to sales I would mention brilliant feature in Google Analytics called GOALS, you can configure it the measure sales quite well. Also it will tell you what does work and what does not.

Statistics define your efforts of your website. Statistics reports your site's overall performance; I check it every day for getting something new trick or idea to increase my website's traffic. Statistics define in which area you work well and which point you should concentrate for getting more profit.