I've done it, my site was quite large that the time and I ran into a few issues with older content. if there's little activity or the sites new I'd say theres not much to be concerned about.
It is very simple to do, your hosting or google will give you instructions

Thanks Abbey - appreciate that information.

Mike, if they stay on the same server and just want to change the domain, all they need to do is change website URI in the config.php file. 

Thanks Ross that is a HUGE help - I could probably do that myself. So basically just point the domain to the hosting, FTP in snag the config.php file and change the website URL, reupload and done? I do not have to worry about links breaking or anything from a database perspective?

Thanks again Ross,

Mike

I had asked Arvixe if they would handle the switch (I just do not personally want to mess anything up) and this is how they had responded, is it really that complicated or is it just simply switching the config.php?:

If we were to change the primary domain on your account for skadate, it may break any database strings or config files that reference your primary domain as an identifier. You would need to be able to fix these in order to resolve any errors that may occur because of the change. If you would like us to go ahead and change the domain, please confirm this action by providing the last four characters of your billing account password.

However, fixing broken database lines and editing the script's config files are not covered under Arvixe's free support scope. We do have a concierge department who charges a fee for this if you'd like to go ahead with that instead.

Yes, all links in the newsfeed would lead to the old domain name as this is info is static and is stored in the database. 

Please read this post: http://www.oxwall.org/forum/topic/11053