Is ghusl or wudu valid if the Basmala or intention is forgotten?

It is sunnah to make an intention and recite the Basmala at the beginning of wudu and ghusl. (Marghinani, al-Hidaya, 1/15-17) Therefore, wudu and ghusl performed without intention or reciting the Basmala are still valid. However, forgetting to make the intention or recite the Basmala before wudu or ghusl results in missing out on the reward of the sunnah.

According to the Shafi'i school, intention is obligatory (fard) in wudu and ghusl, while reciting the Basmala at the beginning of ghusl is sunnah. (Shirbini, Mughni al-Muhtaj, 1/166-167, 222; Ardabili, al-Anwar, 1/69-71)

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu