Hi Marie!
I think you are correct in saying, "If someone linked to you because they liked your store, this is a natural link. KEEP IT!" is very true.
However, wouldn't Google consider this type of linking a link scheme of sorts?
Matt Cutts even says the following on WebProNews.com - “But then there’s also on the manual side,” he continues. “So, imagine that you have a Polish website, and then you see a site-wide link in English talking about, ‘Rent cheap apartments,’ you know. To a regular person, that looks pretty bad. So, certainly it does happen that you have site-wide links – maybe you have a blogroll or something like that, but if I were a manual webspam analyst, sort of doing an investigation, and we got a spam report, you’re an English site, and you’ve got a site-wide Polish link or something like that or vice versa, it looks commercial or it looks off-topic, low-quality or spammy, then that can affect the assessment on whether you want to trust the out-going links from that site.”
The site in question has 3,000+ links coming from that blog website. It appears that each page on the blog is linking to your website via the anchor text treats me well.
I looked at some of the content and the other links on the blog website and they don't seem to correspond with the content or type of site www.jans.com is. I guess if it were me, I would ask the blogger to write a blog about my company and link to it once or twice in the blog article, instead of 3,000+ times in the sidebar navigation.
I am interested in why if you, "... have a fair sized information site for which I do no link building and I regularly get whacked out spammy looking links pointing to it." That you don't try to clean these, "spammy looking" links up?
I understand and completely agree with the mentality of, "If it ain't broke, why fix it?" But from a good SEO standpoint does it not make sense to clean these links up by requesting the webmaster to remove them?
Also, I hope you don't think I am coming off as being hostile or anything. I really like your responses to questions as I know you are extremely knowledgeable in SEO. I am just trying to better myself and become more knowledgeable on the topic.
Thanks for any additional information you can provide!
Mike