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I'm a website developer, and in the past I have usually added a tiny backlink to the footer of my clients' websites like this:

Website Design by MyCompanyName

I understand that Google sees this as a low-quality backlink.  However, I was wondering if such links can hurt my rankings.  Does Penguin sees these links as spam?  If so, should I add a rel="nofollow" to the links?  Is there anything else I should change?

I do not want to remove these links completely because they are good for marketing my business.  I just want to minimize any negative SEO impact of the links.

I appreciate your input.  Thanks.

I agree with eyepaq.  It depends largely on the quality of the links you are generating.  To the best of my understanding, press releases should only be published to a single authoritative site (either your site or a third party, not both).  If you are distributing the same press release to multiple websites, those will likely be counted as duplicate content.  If your site is one of those duplicating the content then your rankings could suffer.

However, if you are producing legitimate back-links from social media, blogs and other viral marketing channels then don't stop.  Your competitors won't stop, and they will keep on moving past you.  SEO (and marketing in general) is never done.

Never stop producing new, useful, engaging, unique content and getting the word out.  Even if your current content ranks well, you should be producing new content that needs to be shared.  I believe Google considers freshness of content as a marker of relevancy, so if all of your content and back-links (especially social) are 3 years old I suspect your rankings could decline.