Over the centuries, many men before Rand al'Thor claimed to be the Dragon Reborn. Only a few could channel, but those few often wreaked havoc before they could be killed or gentled.
TEotW,Ch3 - Padan Fain tells the Emond's Field crowd that there is a false Dragon in Ghealdan. That is the third in the last five years. The last one started a war and laid siege to Illian.
TEotW,Ch26 - News in Whitebridge - the false Dragon Logain was captured near Lugard. Bartim saw the previous false Dragon paraded through the countryside two years ago.
TEotW,Ch34 - The road to Caemlyn is filled with people headed to see the false Dragon Logain.
TGH,Ch25 - Thom's patrons want to hear news about false Dragons.
TDR,Prologue - Pedron Niall is sure that Rand is just another false Dragon. He wonders about the other two in Saldaea and Tear. He plans to use the false Dragon to augment his own position.
TDR,Ch12 - News in Tar Valon - Mazrim Taim has been captured and the false Dragon in Haddon Mirk was captured and executed. The moment Rand declared himself the false Dragons were eliminated.