Should I add
rel="nofollow" to the links from my site menu? (To links like: home, about us, contact etc. that don't have any connection with the site niche.)
Does this helps? What other options do I have?
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NO!! Doing this is SEO suicide. Menu links are great way to channel PageRank to your important pages. Using nofollow would essentially keeping PR from those pages and, even worse, throwing away PR as PR is still "sent" to those links. It's just not used when calculating those page's PR. Don't use nofollow on any internal links unless you don't want search engines finding the pages they are linking to.
If you really want to deemphasize those pages then remove them from your main menu. The biggest issue you will have with that, though, is that they are important pages to users so they need to be easily found. That means you probably want to place them in the footer of your website. That basically is the same as putting them in your main menu.
I wouldn't worry about PR and interlinking to those pages. They may not seem like important pages to you but they are to your users. If you interlink your pages properly then your "really" important pages will stand out from the rest anyway. My advice is to leave those links in your main menu and not worry about it.
@m3tsys: +1 on John Conde's answer.