Bom, ao tentar acessar: http://localhost:8080/Odontonew/tabelas/dentista.jsf ele me redireciona para: Odontonew/tabelas/dentista.jsp.
E obviamente que ao fazer isso ele da página não encontrada pois o dentista.jsp não existe.
Meu web.xml
<?xml version="1.0" encoding="UTF-8"?>
<web-app version="3.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xmlns="http://java.sun.com/xml/ns/javaee" xmlns:web="http://java.sun.com/xml/ns/javaee/web-app_2_5.xsd"
xsi:schemaLocation="http://java.sun.com/xml/ns/javaee
http://java.sun.com/xml/ns/javaee/web-app_3_0.xsd"
id="WebApp_ID">
<display-name>Odontonew</display-name>
<!-- Configuracao do Spring -->
<context-param>
<param-name>contextConfigLocation</param-name>
<param-value>/WEB-INF/applicationContext.xml</param-value>
</context-param>
<listener>
<listener-class>
org.springframework.web.context.ContextLoaderListener
</listener-class>
</listener>
<listener>
<listener-class>
org.springframework.web.context.request.RequestContextListener
</listener-class>
</listener>
<!-- Configuracao DO JSF -->
<servlet>
<servlet-name>Faces Servlet</servlet-name>
<servlet-class>javax.faces.webapp.FacesServlet</servlet-class>
<load-on-startup>1</load-on-startup>
</servlet>
<servlet-mapping>
<servlet-name>Faces Servlet</servlet-name>
<url-pattern>*.jsf</url-pattern>
</servlet-mapping>
<welcome-file-list>
<welcome-file>index.jsf</welcome-file>
</welcome-file-list>
<context-param>
<param-name>javax.faces.PROJECT_STAGE</param-name>
<param-value>Development</param-value>
</context-param>
<context-param>
<param-name>primefaces.THEME</param-name>
<param-value>afterwork</param-value>
</context-param>
<context-param>
<param-name>com.sun.faces.writeStateAtFormEnd</param-name>
<param-value>false</param-value>
</context-param>
</web-app>