To start with, let me tell you blockchain in itself is a data structure. A back-linked list of records.
If we take an example of bitcoin, the blockchain of which is stored in levelDB, which uses a key-value pair database, however you can also consider couch DB.
Hash map is also an option you can consider which is an in-memory data structure,here, the key is a hash of the contents (such as a block header). From there, the header's Merkel root would point to another hash map of transactions arranged in a Merkle tree (as per the protocol).