What are the hardware requirements for running a servlet environment on Linux with Apache, Tomcat, and PostregSQL?
It depends entirely on the application. Most Linux software doesn't publish hardware requirements, which are usually fictions anyway. You can get a development workstation running those components with a 300 Mhz Pentium and 128M of memory, but it won't break any speed records. Requirements go up if you're looking to build an industrial-grade Web server - and you especially shouldn't skimp on the memory (Java can be highly memory-intensive).
To really answer the question, you need to perform load-testing with your application. Until you simulate your real application load, any hardware requirement is just a wild guess.