My team likes to use the previousElementSibling and nextElementSibling methods as it saves them having to filter out TEXT_NODES (which the majority of the time - when sifting through the DOM - they don't have to worry about).
Internet Explorer <= 8 doesn't support either method, but it's current DOM implementation ignores TEXT_NODES (when using previousSibling and nextSibling) so they already act like previousElementSibling and nextElementSibling.
But when checking over my teams code I noticed that they would use a conditional code branching in every instance where they wanted to use previousElementSibling and nextElementSibling, so to try and help keep their code DRY I just used a very basic feature detection script to abstract these methods into two separate functions for them to use instead.
This feature detection assumes the head and a body tags are available at the time of the script executing.