This probably depends on your database, but here is a solution for MySQL 5 that involves using a variable:
SET @a:=0;
UPDATE table SET field=@a:=@a+1 WHERE whatever='whatever' ORDER BY field2,field3
You should probably edit your question and indicate which database you're using however.
Edit: I found a solution utilizing T-SQL for SQL Server. It's very similar to the MySQL method:
DECLARE @myVar int
SET @myVar = 0
UPDATE
myTable
SET
@myvar = myField = @myVar + 1
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