Most of the Web APIs available out there in the web nowadays use some kind of authentication for identifying client applications. Although they implement authentication in different ways, they can be typically categorized in three main groups, services that use Keys, OAuth or HMAC.
Keys is the first scenario and probably the simplest one. Every client application is identified with a simple and fixed application key. This authentication mechanism is perhaps a bit weak, but the data that the service has to offer is not sensitive at all. The data is available for everyone with a key, and it’s pretty much used for public services such as Google maps or a search for public pictures in Instagram for example. The only purpose of the key is to identify clients and apply different SLA (service level agreements) such as api quotas, availability, etc.
HMAC is typically used for consuming sensitive data that is only consumed by his owner and not shared with anyone else. This kind of authentication is typically used in multitenant applications, where a tenant is the owner of the data. This model fits real well with cloud computing where a vendor such as AWS or Windows Azure use a key for identifying the tenant and provide the right services and private data. No matter which client application is used to consume the services and data, the main purpose of the key is to identify the tenant. Hawk is new specification born in this area to standardize how HMAC authentication.
OAuth is last one and probably the most complicated one. It was born with the idea of delegating authorization in the web 2.0. The service who owns the data can use OAuth to share that data with other services or applications without compromising the owner credentials.
The analogy given by Eran Hammer Lahav in this post "Explaining OAuth" is very close to what the specification tries to address,
"Many luxury cars today come with a valet key. It is a special key you give the parking attendant and unlike your regular key, will not allow the car to drive more than a mile or two. Some valet keys will not open the trunk, while others will block access to your onboard cell phone address book. Regardless of what restrictions the valet key imposes, the idea is very clever. You give someone limited access to your car with a special key, while using another key to unlock everything else."
This kind of authentication makes a lot of sense in social media services like Twitter, Facebook, Windows Live or Google to name a few, where the service owns some private data like contacts or pictures that can shared with other applications without putting the user credentials into risk.
OAuth assigns a key to every different client application allowed to consume the data, so the access can easily be revoked by disabling the key associated that client application.