It depends on the type of application you are building, the complexity of the queries and the things your database engine and server lets you do.
If your database service only allows you to make simple SQL queries, less than 20 queries would be fine for a small, common webpage, but if it's the webpage for your university or a decision taking support application, 60 may not be enough.
If you have the privileges and your DBMS is capable (Oracle and such, compared to older versions of MySql for example), more than 20 queries asks that you start creating stored procedures, functions and triggers for the heavy tasks. In many cases you can't, so the number of queries naturally grows and you start using cache to ease the pressure on the server.
Some heavy tasks can be achieved in less queries using subqueries for example, but they are really heavy on the database engine. They aren't really recomended in some cases and should be used with care if they involve thousands of records.
The example up there from Vinko may be true for small, 1 week development "projects", but if you ask about Amazon, they don't use your common PHP / MySQL development package; behind the frontdoor lies a complex system of distributed computing and data-mining algorytms. If you're a newbie you shouldn't take big brothers like that for a reference...