Looking at how people are using COUNT(*) and COUNT(col) it looks like most of them think they are synonyms and just using what they happen to like, while there is substantial difference in performance and even query result. Lets look at the following series of examples:

Suboptimal ORDER BY implementation, especially together with LIMIT is often the cause of MySQL Performance problems. Here is what you need to know about ORDER BY … LIMIT optimization to avoid these problems ORDER BY with LIMIT is most common use of ORDER BY in interactive applications with large data sets being sorted. On many [...]

One nice feature added for EXPLAIN statement in MySQL 4.1 is EXTENDED keyword which provides you with some helpful additional information on query optimization. It should be used together with SHOW WARNINGS to get information about how query looks after transformation as well as what other notes optimizer may wish to tell us. It is [...]