Below is my list of show tunes whose titles refer to remembering or forgetting:  

“Don’t Forget the Lilac Bush” – Street Scene

“Forget About the Boy” – Thoroughly Modern Millie

“Forget All Your Books” – Three’s a Crowd

“I Don’t Remember Christmas” – Starting Here, Starting Now

“I Remember” – Evening Primrose, Rags

“I Remember It Well” – Gigi, Love Life

“I Remember Mama” – I Remember Mama

“It’s Nice Looking Back on the Past” – Lorelei

“I Wish I Could Forget You” - Passion

 “Remember Me” – Little Fish

“Remember That I Care” – Street Scene

“Something to Remember You By” – Three’s A Crowd

“There’s Always One You Can’t Forget” – Dance a Little Closer

“Try to Forget” – The Cat and the Fiddle

“Try to Remember: - The Fantasticks

“Will You Remember Me?” – Knickerbocker Holiday, Lady, Be Good!

  

It’s a modest list, but I trust that we can expand it quickly! I also encourage you to think about lyrics that address memory. As always, you are free to debate titles that I've included here. 

A few lyrics, and a few songs

"Someone in a Tree" from Pacific Overtures
"Where or When" from Babes In Arms
"Tom" from Hello Again
"Remember" from A Little Night Music
the many ballads from Assassins
"The Barber and His Wife" from Sweeney Todd
"At the Ballet" from A Chorus Line