Neo4j:

“Neo4j is a graph database. It is an embedded, disk-based, fully transactional Java persistence engine that stores data structured in graphs rather than in tables. A graph (mathematical lingo for a network) is a flexible data structure that allows a more agile and rapid style of development.
[...]
Neo4j has been in commercial development for 8 years and in production for over 5 years. It is a mature and robust graph database[...]
In addition, Neo4j includes the usual database features: ACID transactions, durable persistence, concurrency control, transaction recovery, and everything else you’d expect from an enterprise-strength database.[...]“

http://neo4j.org/

http://giladmanor.blogspot.com/2009/07/down-rabbits-hole-with-neo4j-part-1.html

mongoDB:

“MongoDB is a high-performance, open source, schema-free document-oriented database.[...]
When we describe MongoDB as “document oriented”, we mean it’s in the class of databases for which the primary storage unit is a collection – possibly structured – of data, most likely as key/value pairs.”

http://www.mongodb.org

Hypertable:

“Hypertable is an open source project based on published best practices and our own experience in solving large-scale data-intensive tasks. Our goal is to bring the benefits of new levels of both performance and scale to many data-driven businesses who are currently limited by previous-generation platforms.”

http://www.hypertable.org/

Dynamo:

“Unlike a relational database, Dynamo is a distributed storage system. Like a relational database it is stores information to be retrieved, but it does not break the data into tables. Instead all objects are stored and looked up via a key.”

http://www.allthingsdistributed.com/2007/10/amazons_dynamo.html
http://www.readwriteweb.com/archives/amazon_dynamo.php

Extra info:

http://www.computerworld.com/s/article/9135086/No_to_SQL_Anti_database_movement_gains_steam_?taxonomyId=173&pageNumber=1&taxonomyName=Databases