I have a particular website that I want to add Google Analytics to, however I don't want it to get indexed because of that. Will adding Google Analytics make Google start indexing my site?
There is no reason for Google to index your website just because of the GA code (it might index it through other methods though, i.e. - links to your site). Moreover, Google obeys robots.txt and the META ROBOTS protocol, so to prevent your website from being indexed by Google, you may upload a robots.txt file with the following instruction
user-agent: googlebot Disallow: /
If you want to disallow all SEs, then replace Googlebot with
*. However, do note that despite adding the robots.txt file, your website will still show up in Google if your URL is searched with but it won't display any content from your website on the search results.
If you want to completely avoid getting into the google index, add the following META ROBOTS tag in the
<header> of all your pages
<meta name="googlebot" content="noindex">
If you don't want to be indexed by any search engines, replace googlebot with
robots in the above meta tag
Google will begin to index your site the moment it finds it, GA installed or not. I suppose adding GA to your site may help them find it faster, but if you do not want your site indexed you need to take explicit steps to stop that from happening with proper no-indexing and a robots.txt file.
It is actually even a little more involved than that, so here is a link to a page where Matt Cutts, from Google, goes into more detail.