Consider this table (from http://www.tizag.com/mysqlTutorial/mysqlmax.php):
Id name type price
123451 Park\'s Great Hits Music 19.
This is the greatest-n-per-group problem that comes up frequently. My usual way of solving it is logically equivalent to the answer given by @Martin Smith, but does not use a subquery:
SELECT T1.Id, T1.name, T1.type, T1.price
FROM Table T1
LEFT OUTER JOIN Table T2
ON (T1.type = T2.type AND T1.price < T2.price)
WHERE T2.price IS NULL;
My solution and all others given on this thread so far have a chance of producing multiple rows per value of type, if more than one product shares the same type and both have an equal price that is the max. There are ways to resolve this and break the tie, but you need to tell us which product "wins" in case like that.
You need some other attribute that is guaranteed to be unique over all rows, at least for rows with the same type. For example, if the product with the greater Id value should win, you can resolve the tie this way:
SELECT T1.Id, T1.name, T1.type, T1.price
FROM Table T1
LEFT OUTER JOIN Table T2
ON (T1.type = T2.type AND (T1.price < T2.price
OR T1.price = T2.price AND T1.Id < T2.Id))
WHERE T2.price IS NULL;