Perhaps better-put: MongoDB solves problems OP doesn't understand because he sees them in terms of purely relational SQL databases.
- Easy to set up (including replication)
- Fast
- Data in "JSON" format (it's BSON internally)
- Javascript (used for map/reduce mainly)
- Good availability of libraries
Theoretically, CouchDB would have been better, but I've heard some bad stories (remember UbuntuOne)?
I don't have much experience with other NOSQL DBs (except for Redis, it's great, but I like to call it a "DB Toolkit" - I'm not dissing it, I love it)