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Don't Create Link Farms
A third way that you can end up penalized is a bit more subtle: if you have pages that have lots and lots and lots of links pointing to other sites, you could have that page categorized as a so-called "link farm", thereby deprecating any value that a link from your site / page could offer someone else (or another of your sites, for that matter).
In the SEO world, the common belief is that you should never have more than 100 outbound links on a page, and 60-75 is a really good number.
The workaround for this is easy: simply take your links page and break it into more pages. If you have 10 pages with 50 links each, the people to whom you're linking are more likely to get a benefit from your link than if you have 2 pages of 250 links. By the same token, having someone link to you from a link farm page is useless and uninteresting. It certainly won't improve your pagerank (see How does Google Figure out What Pages are More Relevant? Pagerank. for more about pagerank).
There are lots of other ways people try to circumvent the Google pagerank system, among other search engines, and there are lots of SEO specialists (really, I should say "specialists") who just use some shareware app to figure out sneaky and short-term fixes to help your relevance and page rank. And you should avoid all of them, because if your site is blacklisted then you'll likely have to change your domain name and/or IP address to even get back into the Google engine at all. It's not a pretty sight (or pretty site!) and the risk is far too high for any short-term reward on Google.