A previous answer only mentioned SSL in the context of data transfer and didn't actually cover authentication.
You're really asking about securely authenticating REST API clients. Unless you're using TLS client authentication, SSL alone is NOT a viable authentication mechanism for a REST API. SSL without client authc only authenticates the server, which is irrelevant for most REST APIs because you really want to authenticate the client.
If you don't use TLS client authentication, you'll need to use something like a digest-based authentication scheme (like Amazon Web Service's custom scheme) or OAuth 1.0a or even HTTP Basic authentication (but over SSL only).
These schemes authenticate that the request was sent by someone expected. TLS (SSL) (without client authentication) ensures that the data sent over the wire remains untampered. They are separate - but complementary - concerns.
For those interested, I've expanded on an SO question about HTTP Authentication Schemes and how they work.