By default mongodb has no enabled access control, so there is no default user or password.

To enable access control, use either the command line option --auth or security.authorization configuration file setting.

You can use the following procedure or refer to Enabling Auth in the MongoDB docs.

Procedure

1. Start MongoDB without access control.

   mongod --port 27017 --dbpath /data/db1
   

2. Connect to the instance.

   mongo --port 27017
   

3. Create the user administrator.

   use admin
   db.createUser(
     {
       user: "myUserAdmin",
       pwd: "abc123",
       roles: [ { role: "userAdminAnyDatabase", db: "admin" } ]
     }
   )
   

4. Re-start the MongoDB instance with access control.

   mongod --auth --port 27017 --dbpath /data/db1
   

5. Authenticate as the user administrator.

   mongo --port 27017 -u "myUserAdmin" -p "abc123" \
     --authenticationDatabase "admin"
   

In addition with what @Camilo Silva already mentioned, if you want to give free access to create databases, read, write databases, etc, but you don't want to create a root role, you can change the 3rd step with the following:

use admin
db.createUser(
  {
    user: "myUserAdmin",
    pwd: "abc123",
    roles: [ { role: "userAdminAnyDatabase", db: "admin" }, 
             { role: "dbAdminAnyDatabase", db: "admin" }, 
             { role: "readWriteAnyDatabase", db: "admin" } ]
  }
)

If you have already created the user, you can update the user as follows:

First log on:

mongo --port 27017 -u "myUserAdmin" -p "abc123" \
  --authenticationDatabase "admin"

The add permissions:

use admin
db.grantRolesToUser(
   "myUserAdmin",
   [ { role: "userAdminAnyDatabase", db: "admin" }, 
     { role: "dbAdminAnyDatabase", db: "admin" }, 
     { role: "readWriteAnyDatabase", db: "admin" } ]
)

For MongoDB earlier than 2.6, the command to add a root user is addUser (e.g.)

db.addUser({user:'admin',pwd:'<password>',roles:["root"]})