ACID and NoSQL are completely orthogonal. One does not imply the other.
I have a notebook on my desk, I use it to keep notes on things that I still have to do. This notebook is a NoSQL database. I query it using a linear search with a "page cache" so I don't always have to search every page. It is also ACID compliant as I ensure that I only write one thing at a time and never while I am reading it.
NoSQL simply means that it isn't SQL. Many people get confused and think it means highly-scaleable-wild-west-super-fast-storage. It doesn't. It doesn't mean key-value store, or eventual consistency. All it means is "not SQL", there are a lot of databases in this planet and most of them are not SQL[citation needed].
You can find many examples in the other answers so I need not list them here, but there are non-SQL databases with ACID compliance for various operations, some are only ACID for single object writes while some guarantee far more. Each database is different.
