They are worth something, but very little. Meaning it would take 100 inbound PR 0 links to equal what you would get from 1 PR 1 link. Thats just a random number off the top of my head of course, not sure of the exact number ratio. As far as "spammy" - try to get inbound links from authority sites on the subject of your site that are related. A PR 3 link from a movie site if you have that same niche is better than a PR 4 link from an automotive site.
If they are relevant links, yes, they have some value, and can help with serps if you use anchor text. Two reasons why a PR0 relevant link is probably worth the time it takes to place it: pages with a PR0 actually have a small fractional PR value, and the page may have PR juice that doesn't show on the toolbar prior to the long-awaited update. Inbound links can't really hurt you, as far as I've been able to tell. The benefit may be too small to be worth it, but every link is some help, if not with Google, then with Yahoo or MSN.
If your link is placed to the link page with PR0, but the home page of the same website is on the top in search results for your keyword that´s good and also valuable.
I've said it before, and I'll say it again: even a though pr0 link might not add value to your site right away, it won't hurt it either. The advantage of a pr0 link is that you get it either cheap or free, and before too long the site might get a high pr. That is why I tell people to target new directories with pr0. Its usually free with no reciprocal required, and most often than not, jumps to an pr3 + at the first update.
The PR 0 sites will gain some PR in the next update if they have links pointing to them. Plus there aren't too many outbound links on the site. A clean and young PR 0 site's link is definitely not counted as spam.
Will we really ever know the truth? I guess everyone is saying, A penny is worth something, but is it worth picking up if your late to an appointment?
PR0 links do have value, because many of the links shown in Webmaster Tools have a Pagerank of 0. Many links form Yahoo answers are from PR0 pages, but they are definitely valuable.
Just a thought. If a site is a PR0 today, what will it be in 6 months or 1 year. All new sites start out as PR0 until they start getting indexed by google. Over time, google will calculate PR for those sites. If the page your link is on goes from PR0 to PR 3, it was a good link. If it stays at PR0 then it is just a link. But to be on a PR0 link page or in a Free-for-all link site, then it is just bad and will get you penalized. I gamble with New PR0 sites that have good design and content. It shows that they should be a good quality link.
The 5 seconds it would take to pick up the penny won't make you that much later unless the appointment person has an atomic clock. And it's not just a penny, it's a penny that might turn into a dime or $10 or $1000 in six months.
Well, as of today anyway, sphinn.com is a PR0 and I wouldn't mind a link from them...which illustrates two points that have already been suggested here. The traffic a site gets (and might then give you) can be as important as the PR, and today's PR0 is tomorrow PR6. Not every PR0 is going to be a sphinn, but you just never know.