Let's say you're developing a site in .NET (lucky you), so your URLs aren't case-sensitive. A page called page.aspx can be reached at PAGE.aspx, Page.aspx, paGE.aspx, etc etc. But you're very consistent -- every time you link to the page, without exception, you use the URL Page.aspx.
Your page becomes rather popular, and other sites start linking to it. But your luck holds, and 100% of the links to your page, both internal and external, refer to it as Page.aspx. Life is sweet.
That is, life is sweet until the owner of the site tells you he doesn't like the way capital letters look in his URLs, and he wants you to change everything to lower-case (personally, I agree with the no-caps rule, but like I said, this is semi-hypothetical). The question is, what's going to happen if you go to your page and stick this in the <head>:
Before we go any further, here's my understanding of link rel="canonical" and what it's for: if a given page can be reached at more than one URL, you use it to let search engines know which of the possible URLs you prefer. Without it, the search engines would look over whatever different URLs are being used to reach the page, see that they were dealing with duplicate content, and decide for themselves which URLs to ignore, leaving just one that they would treat as canonical. This is a common situation with e-com sites, where the same content may be presented in different orders, sorting a list of products by different criteria.
So my question is about how strong a signal it is to use this code. In the hypothetical above (which by the way is not an e-com site, so it doesn't have those obvious issues mentioned above), 100% of hundreds, perhaps thousands of links from a wide variety of domains are all pointing to Page.aspx. Is one line of code telling the search engines you'd rather they count page.aspx as canonical, despite all evidence to the contrary, enough to make a difference? If not, what is? What about if all of your internal links agree with the rel="canonical" choice, but you've got a ton of links from other sites using a different URL -- who wins?