Mail is returning "undeliverable" message to senders.

The mail is getting to my mailbox just fine but it's sending an undeliverable message to senders. Since I've signed up for receiving all my documents online, many companies are sending me snail mail to let me know their messages are undeliverable and killing trees in the process by printing pages of statements I already have online. I use @me.com for my address but my Apple ID is still .mac. I use this ID for three iPods, 2 iPads, an iPhone, MacBook, iMac and older Power Mac. Longtime Mac user, first machine was a 512ke, but this one has me perplexed.