Several SQL implementations now have (years after this question was originally asked) a "vector" type.

• SQLite now has sqlite-vec : a vector search SQLite extension

• MariaDB now has MariaDB Vector

• PostgreSQL now has pgvector

• MySQL now has the VECTOR type; (see also How do I create a field with a vector type in MySQL? and Storing vector coordinates in MySQL )

• Azure SQL Database has the Vector data type

They have some advantages and disadvantages compared to the traditional "bridging table" approach in Nickthename's answer.