Sorry for the ignorant question, but what kind of applications wouldn't require an ACID compliant database server? I have a SQL Server background where ACID has always "been there", and now researching other DBMSs has me thinking. Most every application I can think of would desire either atomicity or isolation. Thanks!
Anything based on a NoSQL-type database is sacrificing ACID compliance in exchange for something, usually speed.
Twitter, Facebook, Reddit, Digg, etc... all are partially non-acid based