How to add a row number to new table in SQL?

I'm trying to create a new table using an existing table already using:

INSERT INTO NewTable (...,...)
   SELECT * from SampleTable

What I need to is add a record number at the beginning or the end, it really doesn't matter as long as it's there.

Sample Table

Elizabeth  RI 02914
Emily      MA 01834

Prospective New Table

1 Elizabeth  RI 02914
2 Emily      MA 01834

Is that at all possible?

This is what I ultimately I'm shooting for... except right now those tables aren't the same size because I need my ErrorTemporaryTable to have a column in which the first row has a number which increments by the previous one by one.

declare @counter int
declare @ClientMessage varchar(255)
declare @TestingMessage carchar(255)
select @counter = (select count(*) + 1 as counter from ErrorValidationTesting)
while @counter <= (select count(*) from ErrorValidationTable ET, ErrorValidationMessage EM where ET.Error = EM.Error_ID)
begin
    insert into ErrorValidationTesting (Validation_Error_ID, Program_ID, Displayed_ID, Client_Message, Testing_Message, Create_Date)
    select * from ErrorTemporaryTable

    select @counter = @counter + 1

end