What are some frameworks for building APIs straight away?

Sails.js (is based on ExpressJS) is a great for creating APIs, saves a lot of time if you're doing a MVP or testing something, and you can use a package to integrate PassaportJS which will give you the ability to use OAUTH2 well integrated to the framework.

I always use Sails when I doing an MVP or a simple API.

First ask yourself if the project really needs its own REST API server. 9 out of 10 times I end up using a BAAS service like parse.com where: user management (auth) is built-in, there is cloud code in case something must be run server-side, the free account is resourceful enough to get you started and then scaling is automatic. There will be limitations of course but if you need something faster than a pre-cooked API repo, that's the way to go.

You can get up and running pretty fast with Eve in Python: http://python-eve.org/.

It has OAuth2 out of the box.

Currently using it for a personal project.

EDIT: formatting.