I know more about mssql that mysql, but I don't think the number of joins or number of rows you are talking about should cause you too many problems with the correct indexes in place. Have you analyzed the query plan to see if you are missing any?
http://dev.mysql.com/doc/refman/5.0/en/explain.html
That being said, once you are satisifed with your indexes and have exhausted all other avenues, de-normalization might be the right answer. If you just have one or two queries that are problems, a manual approach is probably appropriate, whereas some sort of data warehousing tool might be better for creating a platform to develop data cubes.
Here's a site I found that touches on the subject:
http://www.meansandends.com/mysql-data-warehouse/?link_body%2Fbody=%7Bincl%3AAggregation%7D
Here's a simple technique that you can use to keep denormalizing queries simple, if you're just doing a few at a time (and I'm not replacing your OLTP tables, just creating a new one for reporting purposes). Let's say you have this query in your application:
select a.name, b.address from tbla a
join tblb b on b.fk_a_id = a.id where a.id=1
You could create a denormalized table and populate with almost the same query:
create table tbl_ab (a_id, a_name, b_address);
-- (types elided)
Notice the underscores match the table aliases you use
insert tbl_ab select a.id, a.name, b.address from tbla a
join tblb b on b.fk_a_id = a.id
-- no where clause because you want everything
Then to fix your app to use the new denormalized table, switch the dots for underscores.
select a_name as name, b_address as address
from tbl_ab where a_id = 1;
For huge queries this can save a lot of time and makes it clear where the data came from, and you can re-use the queries you already have.
Remember, I'm only advocating this as the last resort. I bet there's a few indexes that would help you. And when you de-normalize, don't forget to account for the extra space on your disks, and figure out when you will run the query to populate the new tables. This should probably be at night, or whenever activity is low. And the data in that table, of course, will never exactly be up to date.
[Yet another edit] Don't forget that the new tables you create need to be indexed too! The good part is that you can index to your heart's content and not worry about update lock contention, since aside from your bulk insert the table will only see selects.