1. Is the Virtual Machine's Network set to the NAT or Bridged?
2. Does the Virtual Machine have Internet/Network Connectivity?
3. Can you PING the Virtual Machine from the Host and visa verse?
Basically if the answer to question 2 is yes, then this really isn't a VMware Player issue per se and you need to troubleshoot/resolve this just as if you were dealing with two Physical Machines.
If the answer to question 3 is no, then temporarily disable firewalls on both the Host and the Guest and try pinging again.
If the answer to question 2 and 3 is yes, then this really isn't a VMware Player issue per se and you need to troubleshoot/resolve this just as if you were dealing with two Physical Machines.
I normally do not use Tomcat however I downloaded Tomcat 6.0.28 and JRE 6u21 and installed both on the Guest and started Tomcat and then had no problem accessing it from the Host using the following convention, http://Guest_IP_Address:8080 and was able to run the examples from the Tomcat Home Page just fine.