There are several artists under this name:

Bebe is a Spanish singer. She was born Bebe Rebolledo in Extremadura, Spain. Her parents were members of the folk group Surberina. Her breakthrough album as a well known artist (in Spain) was entitled Pafuera Telarañas.
She won the Best New Artist award at the 2005 Latin Grammy Awards, and was nominated for five awards total.

BeBe (베베) is also a Korean pop/rock trio. Woo Yeon Ju provide the vocals, Mal Jjang play the guitar and Kim Tae Yoon play the drums. They released their first album, "Be careful!", on Soundholic in 2004.

"BEBE" is also a reggaeton artist from Puerto Rico. He also raps in Spanish.

There's another bebe, a japanese singer who works with Jazztronik