In general, only trust information (input or results) from trustworthy channels. For example, the routines getlogin(3) and ttyname(3) return information that can be controlled by a local user, so don't trust them for security purposes.
In most computer networks (and certainly for the Internet at large), no unauthenticated transmission is trustworthy. For example, packets sent over the public Internet can be viewed and modified at any point along their path, and arbitrary new packets can be forged. These forged packets might include forged information about the sender (such as their machine (IP) address and port) or receiver. Therefore, don't use these values as your primary criteria for security decisions unless you can authenticate them (say using cryptography).
This means that, except under special circumstances, two old techniques for authenticating users in TCP/IP should often not be used as the sole authentication mechanism. One technique is to limit users to ``certain machines'' by checking the ``from'' machine address in a data packet; the other is to limit access by requiring that the sender use a ``trusted'' port number (a number less that 1024). The problem is that in many environments an attacker can forge these values.
In some environments, checking these values (e.g., the sending machine IP address and/or port) can have some value, so it's not a bad idea to support such checking as an option in a program. For example, if a system runs behind a firewall, the firewall can't be breached or circumvented, and the firewall stops external packets that claim to be from the inside, then you can claim that any packet saying it's from the inside really does. Note that you can't be sure the packet actually comes from the machine it claims it comes from - so you're only countering external threats, not internal threats. However, broken firewalls, alternative paths, and mobile code make even these assumptions suspect.
The problem is supporting untrustworthy information as the only way to authenticate someone. If you need a trustworthy channel over an untrusted network, in general you need some sort of cryptologic service (at the very least, a cryptologically safe hash). See Section 11.5 for more information on cryptographic algorithms and protocols. If you're implementing a standard and inherently insecure protocol (e.g., ftp and rlogin), provide safe defaults and document the assumptions clearly.
The Domain Name Server (DNS) is widely used on the Internet to maintain mappings between the names of computers and their IP (numeric) addresses. The technique called ``reverse DNS'' eliminates some simple spoofing attacks, and is useful for determining a host's name. However, this technique is not trustworthy for authentication decisions. The problem is that, in the end, a DNS request will be sent eventually to some remote system that may be controlled by an attacker. Therefore, treat DNS results as an input that needs validation and don't trust it for serious access control.
Arbitrary email (including the ``from'' value of addresses) can be forged as well. Using digital signatures is a method to thwart many such attacks. A more easily thwarted approach is to require emailing back and forth with special randomly-created values, but for low-value transactions such as signing onto a public mailing list this is usually acceptable.
Note that in any client/server model, including CGI, that the server must assume that the client (or someone interposing between the client and server) can modify any value. For example, so-called ``hidden fields'' and cookie values can be changed by the client before being received by CGI programs. These cannot be trusted unless special precautions are taken. For example, the hidden fields could be signed in a way the client cannot forge as long as the server checks the signature. The hidden fields could also be encrypted using a key only the trusted server could decrypt (this latter approach is the basic idea behind the Kerberos authentication system). InfoSec labs has further discussion about hidden fields and applying encryption at http://www.infoseclabs.com/mschff/mschff.htm. In general, you're better off keeping data you care about at the server end in a client/server model. In the same vein, don't depend on HTTP_REFERER for authentication in a CGI program, because this is sent by the user's browser (not the web server).
This issue applies to data referencing other data, too. For example, HTML or XML allow you to include by reference other files (e.g., DTDs and style sheets) that may be stored remotely. However, those external references could be modified so that users see a very different document than intended; a style sheet could be modified to ``white out'' words at critical locations, deface its appearance, or insert new text. External DTDs could be modified to prevent use of the document (by adding declarations that break validation) or insert different text into documents [St. Laurent 2000].