I have tried the same and for me it works. I have done the following:
1. Coded the servlet class TestServlet.java (Didn't use any package).
2. Compiled and placed it in webapps/trial/WEB-INF/classes/ directory.
3. Made following entries into webapps/trial/WEB-INF/web.xml file
4. Started the Tomcat 5.0.19 application.
5. Entered the following URL
http://localhost:8080/trial/TestServlet and Bingo!!! It works.
I believe, in your case there would have been some problem with the web.xml entries. Usually that's the place where most people make mistakes.
Hope it helps.