My friend recently said to me:
Which, I think means "I became sleepy".
But it seems to me that it is the same as saying:
How does the addition of
きた change this phrase?
phirru's comment is almost correct: Addition of
くる in this case means that it happened gradually. It also means that it might not yet be complete. However, the one without
くる does not necessarily mean suddenly. It just does not mention the process. It may or may not have happened suddenly.
いく can be used with similar meaning, but the perspective will be different.
'I am becoming sleepy.'
'I have (gradually) become sleepy.'
'I became sleepy.'