Is it possible to run multiple WordPress sites off of a single VPS? These sites would be completely separate as far as users and content, but I don't know if it's possible to have this for two different URLs.
Looking at the Network documentation, it appears that is used for different sub-domains, but I want to be able to run example.com and test.com as two separate sites but hosted on the same server. Is this possible?
Well you have two options, you can either do vhosting and have separate instances for each domain. This would mean the sites would be completely independent from each other. If you're thinking of selling of a site or moving it to a different vps/server because it's outgrown the current and deserving of it's own server. Also some plugins don't fully support multisites. Drawbacks are this is a high maintance and harder task to do.
Or you can turn your site into a multi site install and then use the Domain Mapping Plugin Pippin has mentioned. This is all round the easier method, you just follow the instructions. And you're users can use the same account on both sites. Depending on your setup multisites can result in a major pain in the ass. However for most people it's just fine.
I believe the Domain Mapping Plugin is what you're looking for :)
If you want physically separate installs, then... yes. You do not need the network feature for that.
I have multiple domains on one vps, some single WP installs, some networks, some with domain mapping, some not.
If you want the easiest and less troublesome way of having multiple sites on one hosting account simply set up separate Wordpress installs using the one database, just change the table prefixes so you don't override a pre-existing Wordpress installation.
Wordpress multisites DO work, but they can be an absolute pain to get working right with multiple domains. Of course after you have installed your separate installations of Wordpress, you'll then need to map each domain to its respective separate copy of Wordpress.
