I'm working on building a RESTful API for one of the applications I maintain. We're currently looking to build various things into it that require more controlled access and security. While researching how to go about securing the API, I found a few different opinions on what form to use. I've seen some resources say HTTP-Auth is the way to go, while others prefer API keys, and even others (including the questions I found here on SO) swear by OAuth.

Then, of course, the ones that prefer, say, API keys, say that OAuth is designed for applications getting access on behalf of a user (as I understand it, such as signing into a non-Facebook site using your Facebook account), and not for a user directly accessing resources on a site they've specifically signed up for (such as the official Twitter client accessing the Twitter servers). However, the recommendations for OAuth seem to be even for the most basic of authentication needs.

My question, then, is - assuming it's all done over HTTPS, what are some of the practical differences between the three? When should one be considered over the others?