How do I create a MongoDB dump of my database?

Use mongodump:

$ ./mongodump --host prod.example.com
connected to: prod.example.com
all dbs
DATABASE: log    to   dump/log
        log.errors to dump/log/errors.bson
                713 objects
        log.analytics to dump/log/analytics.bson
                234810 objects
DATABASE: blog    to    dump/blog
        blog.posts to dump/log/blog.posts.bson
                59 objects
DATABASE: admin    to    dump/admin

Source: http://www.mongodb.org/display/DOCS/Import+Export+Tools

To dump your database for backup you call this command on your terminal

mongodump --db database_name --collection collection_name

To import your backup file to mongodb you can use the following command on your terminal

mongorestore --db database_name path_to_bson_file

You can also use gzip for taking backup of one collection and compressing the backup on the fly:

mongodump --db somedb --collection somecollection --out - | gzip > collectiondump.gz

or with a date in the file name:

mongodump --db somedb --collection somecollection --out - | gzip > dump_`date "+%Y-%m-%d"`.gz

Update:
Backup all collections of a database in a date folder. The files are gziped:

mongodump --db somedb --gzip --out /backups/`date +"%Y-%m-%d"`

Or for a single archive:

mongodump --db somedb --gzip --archive > dump_`date "+%Y-%m-%d"`.gz

Or when mongodb is running inside docker:

docker exec <CONTAINER> sh -c 'exec mongodump --db somedb --gzip --archive' > dump_`date "+%Y-%m-%d"`.gz

This command will make a dump of given database in json and bson format.

mongodump -d <database name> -o <target directory>