There are multiple backup software are available to take yahoo backup. You need to choose right one to take all your emails backup from yahoo server to local drive. I know few utilities for windows that can download all your emails from yahoo server to PST, EML, EMLX, MSG and MBOX file format. if you want to take backup from Yahoo to local hard drive or computer.
Visit here: http://www.backupyahoo.tooutlookconverter.com/
Simple and efficient solutions are available for taking yahoo backup. you can download this Datavare Yahoo Backup Application and convert or export all mailbox items from yahoo to PST, EML ,EMLX, MBOX and MSG file format. You can suggest this application to others.