Github – “Developer Program Member” on Github.com

But I get an error "! [rejected]" and something about "non fast forward"

That's because Git can't merge the changes from the branches into your current master. Let's say you've checked out branch master, and you want to merge in the remote branch other-branch. When you do this:

$ git pull origin other-branch

Git is basically doing this:

$ git fetch origin other-branch && git merge other-branch

That is, a pull is just a fetch followed by a merge. However, when pull-ing, Git will only merge other-branch if it can perform a fast-forward merge. A fast-forward merge is a merge in which the head of the branch you are trying to merge into is a direct descendent of the head of the branch you want to merge. For example, if you have this history tree, then merging other-branch would result in a fast-forward merge:

O-O-O-O-O-O
^         ^
master    other-branch

However, this would not be a fast-forward merge:

    v master
O-O-O
\
 \-O-O-O-O
         ^ other-branch

To solve your problem, first fetch the remote branch:

$ git fetch origin other-branch

Then merge it into your current branch (I'll assume that's master), and fix any merge conflicts:

$ git merge origin/other-branch
# Fix merge conflicts, if they occur
# Add merge conflict fixes
$ git commit    # And commit the merge!

Update 30th, January 2013, 16 months later:

GitHub Blog Post Relative links in markup files:

Starting today, GitHub supports relative links in markup files.
Now you can link directly between different documentation files, whether you view the documentation on GitHub itself, or locally, using a different markup renderer.

You want examples of link definitions and how they work? Here's some Markdown for you.
Instead of an absolute link:

[a link](https://github.com/user/repo/blob/branch/other_file.md)

…you can use a relative link:

[a relative link](other_file.md)
[a relative link](path%20with%20spaces/other_file.md)

and we'll make sure it gets linked to user/repo/blob/branch/other_file.md.

If you were using a workaround like [a workaround link](repo/blob/master/other_file.md), you'll have to update your documentation to use the new syntax.

This also means your documentation can now easily stand on its own, without always pointing to GitHub.

Marcono1234 adds in the comments

Also useful: When the link starts with a /, it is relative to the root of the repository (regardless of whether the markdown file is nested in subdirectories)

Update December 20th, 2011:

The GitHub markup issue 84 is currently closed by technoweenie, with the comment:

We tried adding a <base> tag for this, but it causes problems with other relative links on the site.

October 12th, 2011:

If you look at the raw source of the README.md of Markdown itself(!), relative paths don't seem to be supported.
You will find references like:

[r2h]: http://github.com/github/markup/tree/master/lib/github/commands/rest2html
[r2hc]: http://github.com/github/markup/tree/master/lib/github/markups.rb#L13

As noted in InvisibleWolf's answer, if the target link is a directory and it has space, then you need to use %20 for each space.