You have to symlink various folders that are scattered across the file system to the desired tomcat6 main (or installation) folder.
tsaid suggested symlinking to /usr/share/tomcat6, I rather use /var/lib/tomcat6.
My /var/lib/tomcat6 directory (see the symlinks I've made):
$ ls -g -o /var/lib/tomcat6
lrwxrwxrwx 1 22 2010-07-20 18:15 bin -> /usr/share/tomcat6/bin
drwxr-xr-x 3 4096 2010-07-20 12:22 common
lrwxrwxrwx 1 12 2010-07-20 12:22 conf -> /etc/tomcat6
lrwxrwxrwx 1 22 2010-07-20 18:14 lib -> /usr/share/tomcat6/lib
lrwxrwxrwx 1 17 2010-07-20 12:22 logs -> ../../log/tomcat6
drwxr-xr-x 3 4096 2010-07-20 12:22 server
drwxr-xr-x 3 4096 2010-07-20 12:22 shared
drwxrwxr-x 3 4096 2010-07-20 12:22 webapps
lrwxrwxrwx 1 19 2010-07-20 12:22 work -> ../../cache/tomcat6
Also, don't forget to give full rw permission to your configuration files, in my case in /etc/tomcat6. Since you'll also need to symlink catalina.policy from Catalina/localhost/catalina.policy, don't forget giving execute permission to those folders. You can simplify with full permission to the conf folder, but it's only advised if you're the only user of the computer.
cd /var/lib/tomcat6/conf
chmod -R a+xrw *
Now, delete the entry in Eclipse under Window -> Preferences -> Server -> Runtime Environment and add a new server through Run on Server or anywhere else.