Once you are penalized in Google or probably any other search engine for that matter, it is extremely hard to get back in. While you may be able to get away with bad links linking to your site before getting penalized, but once your site is penalized those bad links can keep you out of the index. So yes, bad links can hurt your site - even if there are just a few.
I'm hoping that this doesn't cause a storm of people now worried about some shady seo linking to them in a spammy way to hurt their rankings. From what I gather from this thread is that once a site has been flagged and penalized that all of the details including on site and off site factors get looked at very closely, much closer than before. Remember that Google has a copy of every page on the web that they've crawled and can quickly pull up any relationships between them. So if on 10/16/07 thirty seven links start appearing with the anchor text "Dining Room Furniture" to a product page on sites that don't monitor their commenter's links, they'll be able to notice it. On it's own this may be ignored as it is generally accepted that external sites cannot hurt your ranking (though that has been removed from Googles documentation) but when coupled with other signals it may add up to something. I would imagine that it also has to be weighed as fraction of the whole of the links. In other words, if a site has 36,000 links to it and 34,000 links are from theme sponsorships, 1,000 are from keyword rich blog comments, 500 are from web directories, and only 10 are from actual sites giving out an editorial link that would be a pretty good sign that someone was trying to improve their ranking by external methods. If 99% of the links are questionable, then it may give them cause to not only devalue them but devalue the site as a whole as well. It's like the interlinking of commonly owned sites problem, or domain farming as its often called. For legitimate sites like Google, youtube, and blogger, some interlinking is possible, but only because if you look at the millions of links they have, only a very small percentage are from their own properites. Where it gets a site into trouble is when the majority of its links are from a common individual that a ranking penalty would make sense. I'm only guessing here and have absolutely no inside knowledge, just trying to talk it out.
All this is derived from Google reps continually insisting that this one site that is penalized remove all the bad links pointing to his site. Once you have bad links and your site is penalized, will Google use those links against you until they are all cleaned up or can you get back in?
What happened to the feeling that bad links can't hurt you too bad? Is this fair? Can this be used to hurt your competitors?
Forum discussion at Google Groups.