MySQL SELECT increment counter

select name,
      @rownum := @rownum + 1 as row_number
from your_table
cross join (select @rownum := 0) r
order by name

This part:

cross join (select @rownum := 0) r

makes it possible to introduce a variable without the need of a seperate query. So the first query could also be broken down into two queries like this:

set @rownum := 0;

select name,
      @rownum := @rownum + 1 as row_number
from your_table
order by name;

for instance when used in a stored procedure.