Join vs. sub-query

In most cases JOINs are faster than sub-queries and it is very rare for a sub-query to be faster.

In JOINs RDBMS can create an execution plan that is better for your query and can predict what data should be loaded to be processed and save time, unlike the sub-query where it will run all the queries and load all their data to do the processing.

The good thing in sub-queries is that they are more readable than JOINs: that's why most new SQL people prefer them; it is the easy way; but when it comes to performance, JOINS are better in most cases even though they are not hard to read too.

In the year 2010 I would have joined the author of this questions and would have strongly voted for JOIN, but with much more experience (especially in MySQL) I can state: Yes subqueries can be better. I've read multiple answers here; some stated subqueries are faster, but it lacked a good explanation. I hope I can provide one with this (very) late answer:

First of all, let me say the most important: There are different forms of sub-queries

And the second important statement: Size matters

If you use sub-queries, you should be aware of how the DB-Server executes the sub-query. Especially if the sub-query is evaluated once or for every row! On the other side, a modern DB-Server is able to optimize a lot. In some cases a subquery helps optimizing a query, but a newer version of the DB-Server might make the optimization obsolete.

Sub-queries in Select-Fields

SELECT moo, (SELECT roger FROM wilco WHERE moo = me) AS bar FROM foo

Be aware that a sub-query is executed for every resulting row from foo.
Avoid this if possible; it may drastically slow down your query on huge datasets. However, if the sub-query has no reference to foo it can be optimized by the DB-server as static content and could be evaluated only once.

Sub-queries in the Where-statement

SELECT moo FROM foo WHERE bar = (SELECT roger FROM wilco WHERE moo = me)

If you are lucky, the DB optimizes this internally into a JOIN. If not, your query will become very, very slow on huge datasets because it will execute the sub-query for every row in foo, not just the results like in the select-type.

Sub-queries in the Join-statement

SELECT moo, bar 
  FROM foo 
    LEFT JOIN (
      SELECT MIN(bar), me FROM wilco GROUP BY me
    ) ON moo = me

This is interesting. We combine JOIN with a sub-query. And here we get the real strength of sub-queries. Imagine a dataset with millions of rows in wilco but only a few distinct me. Instead of joining against a huge table, we have now a smaller temporary table to join against. This can result in much faster queries depending on database size. You can have the same effect with CREATE TEMPORARY TABLE ... and INSERT INTO ... SELECT ..., which might provide better readability on very complex queries (but can lock datasets in a repeatable read isolation level).

Nested sub-queries

SELECT VARIANCE(moo)
  FROM (
    SELECT moo, CONCAT(roger, wilco) AS bar
      FROM foo
      HAVING bar LIKE 'SpaceQ%'
  ) AS temp_foo
  GROUP BY moo

You can nest sub-queries in multiple levels. This can help on huge datasets if you have to group or change the results. Usually the DB-Server creates a temporary table for this, but sometimes you do not need some operations on the whole table, only on the resultset. This might provide a much better performance depending on the size of the table.

Conclusion

Sub-queries are no replacement for a JOIN and you should not use them like this (although possible). In my humble opinion, the correct use of a sub-query is the use as a quick replacement of CREATE TEMPORARY TABLE .... A good sub-query reduces a dataset in a way you cannot accomplish in an ON statement of a JOIN. If a sub-query has one of the keywords GROUP BY or DISTINCT and is preferably not situated in the select fields or the where statement, then it might improve performance a lot.

Sub-queries are the logically correct way to solve problems of the form, "Get facts from A, conditional on facts from B". In such instances, it makes more logical sense to stick B in a sub-query than to do a join. It is also safer, in a practical sense, since you don't have to be cautious about getting duplicated facts from A due to multiple matches against B.

Practically speaking, however, the answer usually comes down to performance. Some optimisers suck lemons when given a join vs a sub-query, and some suck lemons the other way, and this is optimiser-specific, DBMS-version-specific and query-specific.

Historically, explicit joins usually win, hence the established wisdom that joins are better, but optimisers are getting better all the time, and so I prefer to write queries first in a logically coherent way, and then restructure if performance constraints warrant this.

Taken from the MySQL manual (13.2.10.11 Rewriting Subqueries as Joins):

A LEFT [OUTER] JOIN can be faster than an equivalent subquery because the server might be able to optimize it better—a fact that is not specific to MySQL Server alone.

So subqueries can be slower than LEFT [OUTER] JOIN, but in my opinion their strength is slightly higher readability.