"cannot load such file -- nokogiri/nokogiri" (or any other Gem with native extensions on rvm and Ruby >= 2)

After running bundler / gem install I could not load nokogiri lately. It died with cannot load such file -- nokogiri/nokogiri.
This is not a problem of the gem but is due to a broken native extensions installation routine.

When installing nokogiri manually and with verbose output by using gem install -V nokogiri -v 1.5.6, you can see the problem scrolling by when the native extension is built:

Copy/usr/bin//install -c -m 0755 nokogiri.so /home/thomas/.rvm/gems/ruby-2.0.0-p247/gems/nokogiri-1.5.6/lib/home/thomas/.rvm/rubies/ruby-2.0.0-p247/lib/ruby/site_ruby/2.0.0/x86_64-linux/nokogiri

The path were the binary is copied to looks broken. You can fix that by upgrading your RubyGems:

Copyrvm ruby-2.0.0-p247 gem update --system

Delete the gems that failed afterwards, and install them again.