well, you know what, we have been developing sites since the last 2 years...earlier we used to use servlets and now we are using JSP, and while using both the technologies, we never used any Application Servers...we only used a Web Server which is JWS.
You are correct that JSPs compile into Servlets, but sorry to say, but servlets run on Web Servers alone also.
Ofcourse both can run on Application Servers, as Kodark just mentioned above that all application servers are web servers too, hence they can run on an Application Server.
But the statement that "You DO NOT NEED a web server to run jsp pages but you DO need an application server.", is wrong !!!!!!!!!!!