I run my Tomcat, instead I get this "ORACLE DATABASE 10g EXPRESS..." message

You try to run  Apache Tomcat, but instead you  get this message "ORACLE DATABASE 10g EXPRESS EDITION LICENSE AGREEMENT".
This simply means
If you bump into this problem, you have an Oracle 10g Express Edition (OracleXE 10g) installation sitting on the same port as your Tomcat default port (TCP/IP port 8080). As the TCP/IP protocol doesn't allow you to have more than one process listening to the same port (except when you use the advanced channel/selector), then when you start Tomcat, it will fail. You might not be aware that your Tomcat has failed to start, until you get into that message mentioned above.

There are 2 cures to this symptoms, the first cure  is to let Oracle XE take the port, and we move the tomcat installation to another port. The second cure is to set the Oracle XE to use another port.

To achieve the first one, you need to modify your $CATALINA_HOME/conf/server.xml file. Find the portion of the file that contains this snippet (assuming you are using the standard Tomcat installation):

[sourcecode lang="xml"]
connectionTimeout="20000"
redirectPort="8443" />
[/sourcecode]

Change the port 8080 to something else, e.g. 8484.

[sourcecode lang="xml"]
connectionTimeout="20000"
redirectPort="8443" />
[/sourcecode]

By now you should be able to run you application.
Don't forget that you have to run it from port 8484. So if the application you deploy is someapp.war the URL that you aim should be http://localhost:8484/someapp/ instead of http://localhost:8080/someapp/

Ok, now if you want to take the second cure, go to your Oracle XE 10g console using sqlplus. Replace mypassword with that your SYS user password (as specified during the installation process). Note that the number 2, 3, 4 at the left side is generated by the sqlplus tools prompt (you don't need to type them in).

[sourcecode lang="sql"]
C:\> sqlplus sys/mypassword@xe as sysdba
SQL*Plus: Release 10.2.0.1.0 - Production on Thu Jun 18 17:53:47 2009
Copyright (c) 1982, 2005, Oracle. All rights reserved.

Connected to:
Oracle Database 10g Express Edition Release 10.2.0.1.0 - Production

SQL> begin
2 dbms_xdb.sethttpport('8484');
3 end;
4 /
[/sourcecode]

Oracle XE should reply:

[sourcecode lang="sql"]
PL/SQL procedure successfully completed.
[/sourcecode]

After that check to ensure that the configuration has been changed properly:

[sourcecode lang="sql"]
SQL> select dbms_xdb.gethttpport as "HTTP-Port is " from dual;
[/sourcecode]

You should get a message like this:

[sourcecode lang="sql"]
HTTP-Port is
------------
8484
[/sourcecode]

Exit from sqlplus by typing "exit" at the prompt.

If everything as expected, now you can start the Tomcat server and use the port 8080 for Tomcat. To access the Oracle XE 10g database web console, access through http://localhost:8484/apex