What is the easiest way/method/software to dump MySql databases from one server and import into a new Linux server?

What I want to achieve is an easy fool proof quick'ish way of transferring the databases so that they can be run from the new server

Thanks

Hold fire I think I've sorted it using MySql Workbench

Opened old server connection
Exported schema dbname
Created new connection to new server and MySQL
Imported schema dbname and chose option 'New Schema'

Does that sound ok?

yes sounds ok, I have found the export/import to be fairly painless using MySQL workbench

Thanks Huw,

Yes it went painlessly enough, quite easy to do as long as you remember to click the option to create a new schema when importing for the first time rather than overwrite the previous database you imported
I had one issue with one database but again easy enough to resolve by exporting the database first as separate tables, creating a new schema when importing the first table, then adding a table at a time to that schema until the one causing the error flagged up.
Quick'ish fix and soon sorted [^]