Why do editors such as BBEdit and Textmate have the option of ending your file in a newline (line break)? Why is that important?
This is probably because some other users of files require  complete lines

e.g. C code will complain if there is no newline at the end of file - see this SO question

and one main use of Bbedit etc is programming

So the reason is not really specific to the Apple editors mentioned but more for what use the files is made of.

Also see the comment to that question 


  Not really the reason, but it's very annoying if you cat a file and it does not have a trailing newline as the new shell prompt will appear after the last line of the file (i.e. not in column 0)