Though this is years old question...
In short, you can understand ACID as guarantee of data integrity/safety in any expected circumstances.
As like in generic programming, all the headaches comes from multi-threading.
The biggest issue on NoSQL is mostly ACI. D(urability) is usually a separated issue.
If your DB is single-threaded - so only one user can access at once -, that's natively ACI compliant. But I am sure virtually no server can have this luxury.
If your DB need to be multi-threaded - serve multiple users/clients simultaneously - you must need ACI-compliant transaction. Or you will get silent data corruption rather than simple data loss. Which is a lot more horrible. Simply, this is exactly same with generic multi-threaded programming. If you don't have proper mechanism such as lock, you will get undefined data. And the mechanism in DB called fully ACID compliance.
Many YesSQL/NoSQL databases advertises themselves ACID-complient, but actually, very few of them are really does.
No ACID compliance = You will get always undefined result under multi-user (client) environment. I don't even think what kind of DB does this.
Single row/key ACID compliant = You will get guaranteed result if you modify only single value at once. But undefined result (=silent data corruption) for simultaneous multi row/key update. Most of currently popular NoSQL DBs including Cassandra, MongoDB, CouchDB, … These kind of DBs are safe only for single-row transaction. So you need to guarantee your DB logic won't touch multiple rows in a transaction.
Multi row/key ACID compliance = You will always get guaranteed result for any operation. This is minimal requirements as a RDBMS. In NoSQL field, very few of them does this. Spanner, MarkLogic, VoltDB, FoundationDB. I am not even sure there's more solutions. These kind of DBs are really fresh and new, so mostly nothing is known about their ability or limitation.
Anyway, this is a comparison except D(urability). So don't forget to check durability attribute too. It's very hard to compare durability because range becomes too wide. I don't know this topic well…
No durability. You will lost data at any time.
Safely stored on disk. When you get COMMIT OK, then the data is guaranteed on disk. You lost data if disk break.
Also, there're difference even on ACID compliant DBs.
Sometimes ACID compliant / you need configuration / no automatic something.. / some components are not ACID-complient / very fast but you need to turn off something for this... / ACID-compliant if you use specific module... = we will not bundle data safety by default. That's an add-on, option or separated sold. Don't forget to download, assemble, setup and issuing proper command. Anyway, data safety may be ignored silently. Do it yourself. Check it yourself. Good luck not to make any mistake. Everyone in your team must be flawless DBA to use this kind of DB safely. MySQL.
Always ACID compliant = We don't trade data safety with performance or anything. Data safety is a forced bundle with this DB package. Most commercial RDBMS, PostgreSQL.
Above is typical DB's implementation. But still, any other hardware failure may corrupt the database. Such as memory error, data channel error, or any other possible errors. So you need extra redundancy, and real production-quality DB must offer fault tolerance features.
No redundancy. You lose all data if your data corrupted.
Backup. You make snapshot copy/restore. You lose data after last backup.
Online backup. You can do snapshot backup while the database is running.
Asynchronous replication. Backup for each second (or specified period). If machine down, this DB guaranteed to get the data back by just rebooting. You lose data after last second.
Synchronous replication. Backup immediately for each data update. You always have exact copy of original data. Use the copy if origin breaks.
Until now, I see many DB implementation lacks many of these. And I think if they lacks proper ACID and redundancy support, users will lose data eventually.
Best Answer
The important thing to remember here, is that a commonality NoSQL databases tend to share, is that a query-based approach needs to be taken with respect to table design. The main driver for that, is going to be around how the data is queried.
Another consideration is around each data store's adherence to the CAP theorem. NoSQL tends to side with the P of partition tolerance, and then also choose another side. If the NoSQL products support different sides of CAP (AP vs. CP), you'll need to figure out if the overall application is more dependent on consistency or availability.
I would also consider if search is a part of the application, or rather, if the queries require any pattern matching. Some data stores handle this better than others, so it would be good to understand how each functions in those use cases.