Well, no, they’re not “necessary,” if by necessary you mean do they keep your blog alive. But they are necessary if you want people to be able to access your feed, and get your site with styled content rather than pure HTML, and pingback your articles, etcetera. Yeah, your site will work without them, but it’s probably best to leave them there. :o)
The “alternate” relationship link is one that specifies alternative versions of the webpage. The most common use is to specify feeds of the webpage, however it can also be used to say where mobile phone optimized versions are, alternate language versions, etc.
There’s a lot of links that you probably do indeed want to keep.
“stylesheet” specifies the location of the CSS file to display the page properly.
“pingback” specifies the pingback url, allowing other blogs to send you pingbacks when they comment on your posts.
“EditURI” allows you to use external blog editing programs.
“archives” specifies locations of your other posts, to help search engine spiders out.
“microsummary” is a new one for Firefox that lets your Bookmark in browsers show your latest post name (or whatever you want). There’s a plugin to do this sort of thing.
There’s also stuff in meta tags that you may not be familiar with. Anyway, all this stuff is optional, but useful.
