Video games storing player data are a great example of nonrelational data. I'm intending on writing a blog post after I finish my game detailing the structure of data I store and why it was so perfect for mongodb.
* Trading in game items between two users (needs multi document atomic locks if you don't want duplicate or lost items) assuming your "schema" is a document per user
* You want to rename or restructure an attribute in the future, with no schema it's not possible change migrate data easily without writing ad hoc code (maybe you can use third party tools) or changing queries to expect data in multiple "schemas" which quickly gets painful
Good Luck!
You can have schemas with MongoDB. There are various libraries to facilitate database design by schema specification.
Also renaming or restructuring your data is not necessarily an easy task with SQL. The nature of a database dictates that how good it works for your application depends on up to how well thought-out your schema is. Having to change your schema around is tasking. One of the reported advantages of document stores when they were becoming trendy was that it was easy to change your schema since your schema is essentially determined and regulated at the application layer.
Also MongoDB has ACIDic transactions now (freaking finally) so if it’s as-advertised then I feel like half of your argument is not really a strong one any more.
So yes, it's annoying for a very small % of what I'm doing, but 99% of my updates/writes are within a single document, so I find it very nice for development.
A simple example would be a marketplace.
Player buys item X with Y gold from another player.
1. Server checks that item X exists.
2. Server checks that the player has at least Y gold.
3. Server removes the gold from the player
4. Server gives gold to the seller.
5. Server removes item from marketplace.
6. Server adds item to inventory.
What if someone maliciously crafts two requests in a way that step 2 of the second request happens before step 3 of the first request? The money is deducted properly but the account can now have a negative balance and there are now two instances of the item.