It's proprietary and therefore not an option for everyone, but SQL Server's "Filestream" feature [1] was designed for the "large blob of unstructured data" use case (small blobs of unstructured data generally work fine in regular tables). It stores large blob data efficiently in individual files directly on disk that are still managed by the database engine and written/read in the same transaction as table data. It's well-integrated with their other standard features such as backups, HA clusters, etc. It's a pretty impressive feature.
Postgres has the BLOB functionality, but also has the JSONB data type that not only stores structured JSON data efficiently, but also allows indexing on the contents of that data. So you can use BLOBs and explicitly store in the table what you need to search on, or else you can avoid that and take the pseudo-NoSQL route and store indexed JSON.
[1] https://technet.microsoft.com/en-us/library/bb933993(v=sql.1...