Elara DB is an easy to use, lightweight NoSQL database written for python that can also be used as a fast in-memory cache for JSON-serializable data. Includes various methods and features to manipulate data structures in-memory, protect database files and export data. Can serialize and dump to disk for storage and restoration. Integrity checking built in.

Not a server, it's an embedded database.

Redis is another key-value datastore (a distributed hash table, if you like) that can be used for either caching of often used objects or a database to build applications on top of. Can handle just about any serializable data structure, from strings to sets. Clusterable - uses master/slave replication. Written in C but has bindings for any programming language you're likely to know.

Cayley is an open source graph database application, suitable for network mapping or storing graph-like data. Sits on top of NoSQL database servers. Written in Go. Has its own REST API server, query editor, and query visualizer. Supports multiple query languages. Can use multiple back-end databases to actually store the data.

github repo for a nosql database written entirely in and for python as a module. Zero external dependencies, no server. Document oriented database, fully test coverage, less than 1.5kloc. Anything that can be represented as a document can be accessed as a dict. Written in pure Python.