Update: Clarified and corrected explanation.
Isolation levels just indicate how much of your transaction is affected by other concurrent transactions. The higher the isolation level, the less affected it is.
The effort will be made manifest in cpu load, memory load, and perhaps commit latency. In addition, write conflicts can be more likely in higher isolation levels, which may mean that you have to abort your transaction and retry the whole thing. (This only affects transactions that perform updates or inserts, not transactions which only perform selects.)
In general, the rule of thumb is to use the lowest level that gives your application the consistency it needs.
The partial transaction isolation provided by Read Committed mode is adequate for many applications, and this mode is fast and simple to use; however, it is not sufficient for all cases. Applications that do complex queries and updates might require a more rigorously consistent view of the database than Read Committed mode provides.
The Serializable mode provides a rigorous guarantee that each transaction sees a wholly consistent view of the database. However, the application has to be prepared to retry transactions when concurrent updates make it impossible to sustain the illusion of serial execution. Since the cost of redoing complex transactions can be significant, serializable mode is recommended only when updating transactions contain logic sufficiently complex that they might give wrong answers in Read Committed mode. Most commonly, Serializable mode is necessary when a transaction executes several successive commands that must see identical views of the database.
( http://www.postgresql.org/docs/8.4/interactive/transaction-iso.html is very nice. )