This is a tricky one, I have the following output:
mysqldump: Got error: 1045: Access denied for user \'root\'@\'localhost\' (using password: YES) when tr
For MAMP PRO users (or anyone who's mysql is in a weird location) be prepared to specify the mysql full path from the boonies and also specify full path to your user local folder where you want to dump the file or you'll get the "permission denied error"..
Following worked for me after 3 hours of research:
/Applications/MAMP/Library/bin/mysqldump -u root -proot YOUR_DB > /Users/YOUR_USER/yourdump2.sql