As opposed to being stored in Google/Facebook's databases? I don't know if blockchain is the answer, but I would prefer not to trust any of these large corporations and use a decentralized identity system where no third-party has control of my identity information.

In self sovereign identity systems based on verifiable claims, attributes are attested through signed claims on digital identifiers that the user control (e.g. a public key). Blockchains here are the most effective mean to implement claim revocation: if someone who produced a claim wants to revoke it, he writes that on a blockchain.