If I have deleted some pages on my website six months back and blocked these pages using Robots.txt, can that non-existent page show up on Google?
It is possible though unlikely that page content would be cached for this long on some Google servers.
If you want to make sure this content goes away from Google entirely, you should sign up for a Webmasters account and verify your site. From there you can ask Google to remove the content from the cache. Check this article for more information: http://support.google.com/webmasters/bin/answer.py?hl=en&answer=1663416
Robots.txt does not actually prevent Google from indexing a page, it just prevents Googlebot from crawling it. Google may choose to index pages in robots.txt if they believe the page is important enough and they can tell something about the page from links that point to it. Here are two cases in which Google has put forward for doing so
When Google indexes a page without crawling it, it tends to make up the title based on external links. It usually won't have a description or a cached version.
If you put a page that had been indexed into robots.txt, googlebot will stop crawling it, however the decision to stop indexing it may happen much later. Google may be happy indexing the page until it feels that what it crawled is sufficiently out of date. It may continue to index it indefinitely.
If you want to remove a page from the index, you should either do so through webmaster tools or use the robots noindex meta tag.
Google views robots.txt as a "do not crawl" directive, but not a "do not index" directive.