ROW_NUMBER() in MySQL

Is there a nice way in MySQL to replicate the SQL Server function `ROW_NUMBER()`? For example: SELECT col1, col2, ROW_NUMBER() OVER (PARTITION BY col1, col2 ORDER BY col3 DESC) AS intRow FROM Table1 Then I could, for example, add a condition to limit `intRow` to 1 to get a single row with the highest `col3` for each `(col1, col2)` pair.