The majority of the scholars agree that Wudhu is correct even without saying Bismillaah, while some of the scholars hold that the Tasmiyyah is obligatory, so long as one knows and remembers it, based upon what was reported from the Prophet (salallaahu 'alaihi wassallam):
áÇó æõÖõæúÁó áöãóäú áóãú íóÐúßõÑö ÇÓúãó Çááåö Úóáóíúåö
"There is no Wudhu for the one who does not mention the name of Allah upon it." [At-Tirmithi no.25 and Ibn Majah nos.397, 398, 399.]
But whoever left it due to forgetfulness or ignorance, his Wudhu is correct, and he does not need to repeat it, even if we accept that the Tasmiyyah is obligatory, because it is excused due to ignorance or forgetfulness, and the proof for that is in Allah’s words:
ÑóÈøóäóÇ áÇó ÊõÄóÇÎöÐúäóÇ Åöä äøóÓöíäóÇ Ãóæú ÃóÎúØóÃúäóÇ
"Our Lord! Punish us not if we forget or fall into error." [Al Baqarah: 286]
And it has been authentically reported from the Messenger of Allah (salallaahu 'alaihi wassallam) that Allah, the Most Glorified, Most High has answered this supplication.