Question

Every once in a while I will see a bunch of <link> elements in code:

<link rel="Home" href="/" title="Page d'accueil de Babysun" />
<link rel="Index" href="/" />
<link rel="Top" href="/" title="Babysun / Accueil Babysun - Babysun" />
<link rel="Search" href="/content/advancedsearch" title="Recherche Babysun" />
<link rel="Shortcut icon" href="/extension/ezwebin/design/babysun/images/favicon.png" type="image/x-icon" />
<link rel="Copyright" href="/ezinfo/copyright" />
<link rel="Author" href="/ezinfo/about" />

The link element is described as:

The <link> tag defines the relationship between a document and an external resource. The <link> tag is most used to link to style sheets.

(emphasis mine)

What external resources? SEO?

If so, what does Google care about:

<link rel="Home" ...>
<link rel="Index" ...>
<link rel="Top" ...>

Answer 1

rel is not limited to the <link> tag, it can also be used with <a>.

According to the w3c

This attribute describes the relationship from the current document to
the anchor specified by the href attribute. The value of this
attribute is a space-separated list of link types.

You can find the common link-types here :

http://www.w3.org/TR/html4/types.html#h-6.12

And even in these, only the SEO ones (nofollow, noindex, canonical) have some real leverage (although Google is known to ignore them when he wants to.)

This sentence summarizes well the types :

User agents, search engines, etc. may interpret these link types in a
variety of ways. For example, user agents may provide access to linked
documents through a navigation bar.

This being quite a mess, the Microformats project tries to standardize their usage (Microformats are not limited to rel.) You can find draft and specs here. The coolest one is rel="tag" (here).