Ofrcourse it affects the speed. All you basically do is add more records to be checked, and each record in the first table can match with any number of records from the other tables...
Ideally you wouldn't use joins at all.
The only problem is, if you don't use joins (ie: you don't split up your data) you end up with tables that are so huge and cramped will of columns that you can't work with them anymore, let alone understand what it was you were doing :-)
Use as many joins as you need to use, but think about what data you need and how that data is organised in your database. If you need to do four joins to find out a person's last name, you have a problem.