Like with many other burning SEO questions, there is no definitive answer as to whether sitewide links are good or bad.
If we for just a second forget about search engines, we will see that, on the one hand, sitewides can be good for very important links (as users are much more likely to click them), besides they make the overall site template look more consistent (encouraging users to feel more secure).
On the other hand, because of them the site might lack diversity (getting bored with one and the same content throughout the site, the visitors might want to leave soon).
Now, when talking about SEO, the usage of sitewide links may also be highly controversial:
Do external sitewide links leak more PR?
The whole idea that external links hurt the site seems not completely right. While many SEOs will most probably argue my point here, I wouldn’t consider “PR leakage” as the major factor deciding whether sitewide links should be used or not.
I for one try to refrain from linking out using sitewides for the simple reason that these external links do not seem so important that I would want my visitors to click them by all means.
Do sitewide links count as one link or as many links?
Neither, I would say. They can’t be counted as one link as they come out from pages with different authority. At the same time they can’t be equal to the credit you get from multiple-domain links as that’s only one person / resource crediting your site instead of multiple webmasters / resources agreeing on its overall worthiness.
In general, I believe, Google distinguishes them as something very different from the both (recognizing template-based links). They definitely give some credit and aren’t completely worthless:
Sitewides, by their nature, go beyond editorial comment and suggest a special relationship between sites to Google.
Are external sitewide links worthless?
No (see the above). All in all, just like with reciprocal links, if your link profile includes a few solid sitewide inbound links along with other in-link types, that’s very good.
Are sitewide links counted equally to links from same-IP domains?
That would be to say that many sites on one IP are counted as one and the same website. In reality everything is much more complicated. Though no one is sure how exactly this works but I am pretty sure Google first makes sure that all sites on one IP belong to one person before starting to treat all out-links from all his sites as something less useful than many links from many sites.
Are multiple links from the same domain different from templated sitewide links?
Yes, definitely. Again, Google does recognize template-based elements and treat them differently.
Do sitewide links send a signal that the link(s) are purchased?
Yes, I believe, that’s one of multiple signals; thus, they will be seen as paid only if there are other signals (e.g. irrelevance) coming into play.
Do sitewide in-links automatically trigger Google penalty?
No, in this case, everyone would be penalized by now Many factors (your site age; many “bad” sites linking in; the whole network of websites linking in, etc) should come into play. However the sudden spike in sitewide links may be one of the signals that your site is playing against the rules.
To put it smarter:
The overall health of the backlink profiles involved will make a big difference here.