We scored as many goals as them.
We scored as many goals as they did. (correct form, the form above is very common in informal spoken language, it's incorrect though)
Sam and I were present. OK
Can you sing as well as them.
Can you sing as well as they can?
Let you and I try what we can do
Let you and ME try what we can do.
Wait for Harry and me. OK
You know that as well as me
You know that as well as I do.
It was me that gave you the alarm OK
Between you and I, I do not believe him
We are not so poor as them
We are not so poor as they are.
Sam is as old as me
Sam is as old as I am.
He is known to my brother and me
He is as good as me
He is as good as I am.