This option is required by any serious blog publisher, as anybody who wants to rely upon the accuracy of the visitor meter of choice is certainly going to want to see information about their readers - without the distraction of their own activity.
The "Don't track your own pageviews" setup wizard explicitly warns us
In order to do this, Blogger must add a tracking cookie to your browser.Here, we see another instance of the well known need for us to check our browser and computer, thoroughly, for any cookie restrictions.
(Update 2016/03): Blogger has rewritten the Stats "Don't track" dashboard page, which now runs as the blog URL, and no longer requires third party cookies. Now, "Don't track" requires scripts, run under the URL of the blog.
The "Don't track ..." option is on the dashboard Stats "Overview" tab.
Look for the "Don't track your own pageviews" link, to the right of the activity graph on the Stats "Overview" sub menu. You will need to do this separately for each browser, on each computer, that you use.
If "Don't track ..." does not always work, look at cookie and script filters.
If you're watching your Stats displays carefully, you selected "Don't track my pageviews", and you notice that your pageviews are still being included in your Stats displays, you're going to need to examine your browser and your computer settings, for any cookie and script restrictions, and correct any settings, as necessary.
Since this is another feature that's enabled using a script run from "Blogger.com" and read from "Blog*Spot.com" (or whatever country code alias that affects you / custom domain your blog is published under), you're going to have to check the "third party cookies" browser setting, to start. Next, check that you have cookies from "Blogger.com" set to "Permanent", not to "Session".
If you can't find settings in the browser, look on the computer and network.
If the problem is not solved by enabling "third party cookies", and setting "Blogger.com" cookies as "Permanent", check the computer and the network, for any anti-virus, firewall, security appliance, or security suite, which might contain a cookie or script filter. And, do not clear cookies, without considering the consequences.
If your country is subject to aliasing, check for filters to pass the alias.
If access to your blog is subject to Country Code Aliasing, setup your filters to permit the CC Alias of "blogspot.com", for your location. Any filters on your computer need to allow the proper trust level, for your local alias of "blogspot.com".
Blogger cannot code around filter problems on your computer.
This is a problem which only you, the blog owner, can correct - and it's one which Blogger cannot code around.
Since this setting is specific by individual browser, it's going to be a constant challenge for people with multiple browsers and computers - as well as for people with mobile / pocket computers / smart phones. And it may be a problem that will require you to increase your technical skill level.