I heard that .gov and .edu sites links are very important and give boost to your website but i want to ask you all is it possible to get links from .gov website or blogs because these are usually property of government.

The Edu and Gov domains tend to have a lot of security measures because they contain a lot of personal information about the citizens at times.Becoming an expert in the subject matter you want to gain the gov link in, will put you one step ahead of others seeking to win these links.

.edu and .gov sites are not from mars and you can certainly get links from them but Google is not biased with links. It doesn't really matter whether links come from .edu or .gov. or some other extension.

Also, I have heard that they are nofollow and hence won't pass any backlinking credit.

But if you are really intent on doing it, you can prefer Keyword Country to find .edu and .gov sites for backlinking.

To do  this, install the SEO Toolbar for Firefox and click on the "Highlight nofollow links" button to instantly highlight all "nofollow" links in red highlighting. Balance your efforts between both "dofollow" and "nofollow" link building, however, to ensure that your inbound link profile looks natural in Google's eyes.

When using the suggested search queries above, be sure to find out whether the links in comments (either the commenter's name or embeded links within the comments) are "dofollow" or  "nofollow."

To get links from .edu would be easy but we can't get link from .gov site because it is property of government and they keep distance from spamming.

I have heard that they are not very valuable links anyway, even on the high PR sites. I imagine, as stated above, that this is because they are nofollow.