Yes, REMEMBER is a Scrabble word!

Letter values in Scrabble US: R 1, E 1, M 3, E 1, M 3, B 3, E 1, R 1.

Is it a valid word?

REMEMBER is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

recall knowledge from memory; have a recollection
keep in mind for attention or consideration
recapture the past; indulge in memories
show appreciation to
mention favorably, as in prayer
mention as by way of greeting or to indicate friendship
exercise, or have the power of, memory
call to remembrance; keep alive the memory of someone or something, as in a ceremony

Also: call back, call up, think of, think back.