I have a spreadsheet with a list of names on a waiting list, and I have each
row numbered incrementally using the formula =A1+1 etc.  However, when I
delete a row (when someone 'drops out' of the waiting list) the row numbers
below come up with an error (#REF!).

I have also tried to number the rows using Excel's automatic list, but when
I remove a row the row number also disappears (ie row number 9 follows
straight after 7, rather than changing to 8).

What I would like the spreadsheet to do is this:

I have a list:

1 John Smith
2 Joe Blogss
3 Katie Merryfield
4 Ian Jones
5 Carl Huges
6 Doris Brown
and so on...

When Ian Jones says he wants to be removed from the waiting list, I need to
delete his row so that the sheet now says:

1 John Smith
2 Joe Blogss
3 Katie Merryfield
4 Carl Huges
5 Doris Brown

Please could anyone tell me how to do this?  Any help is much appreciated.  
I have been scanning this and other sites, and my Excel Formula 'bible', but
can't find out how to do this seemingly simple thing!

Many thanks