What type of attacks are there that do not use open TCP or open UDP ports?
Is it safe to assume that no open ports means no remote access?
(Excluding the possibility that there is a badware already on the machine that makes outgoing connections to send/receive data/instructions)
Edit: Looks like we also would have to disable ICMP to (help) prevent Denial Of Service type attacks and the possibility of buffer overflow or other undiscovered attacks. Also the possibility that the server would receive a spoofed ping that then sends the response to a third party victim for Denial Of Service
Edit: Looks like one should also look at good-ware "that makes outgoing connections to send/receive data/instructions" such as DNS. The DNS server instructs the UNIX machine what other machines to connect to and send/receive data for. One has to make sure that the DNS server is not hacked and the routers on the way are not hacked.
Edit: I am specifically referring to network attacks in this question. As far as client-side attacks (cookies, social engineering, XSS, etc.) that is not for this question.
Edit: I am attempting to (hopefully fully) secure the servers so that they (theoretically) will not need a firewall. Firewalls are intended but not part of this question.