When do you use each MySQL index type?
For really large table
The primary key is - as the name suggests - the main key of a table and should be a column which is commonly used to select the rows of this table. The primary key is always a unique key (unique identifier). The primary key is not limited to one column, for example in reference tables (many-to-many) it often makes sense to have a primary key including two or more columns.
A unique index makes sure your DBMS doesn't accept duplicate entries for this column. You ask 'Foreign keys?' NO! That would not be useful since foreign keys are per definition prone to be duplicates, (one-to-many, many-to-many).
Additional indexes can be placed on columns which are often used for SELECTS (and JOINS) which is often the case for foreign keys. In many cases SELECT (and JOIN) queries will be faster, if the foreign keys are indexed.
Note however that - as SquareCog has clarified - Indexes get updated on any modifications to the data, so yes, adding more indexes can lead to degradation in INSERT/UPDATE performance. If indexes didn't get updated, you would get different information depending on whether the optimizer decided to run your query on an index or the raw table -- a highly undesirable situation.
This means, you should carefully assess the usage of indices. One thing is sure on the basis of that: Unused indices have to be avoided, resp. removed!