Canonical 23-character answer:

tr A-Za-z N-ZA-Mn-za-m

Ruby - 60 57 38 37 chars

Edit: And just realised Ruby strings have a tr method.

puts$<.read.tr'A-Za-z','N-ZA-Mn-za-m'

Test

input = "The challenge: To read an input of arbitrary length and produce the ROT13 of the input. All characters besides A-Z should be copied to the output verbatim, and case should be preserved if possible.

Any language that can read and write standard streams is fair game."

output = `echo '#{input}' | ruby golf-rot13.rb`

puts "Input:"
puts input
puts "-------"
puts "Output:"
puts output

Gives:

Input:
The challenge: To read an input of arbitrary length and produce the ROT13 of the input. All characters besides A-Z should be copied to the output verbatim, and case should be preserved if possible.

Any language that can read and write standard streams is fair game.
-------
Output:
Gur punyyratr: Gb ernq na vachg bs neovgenel yratgu naq cebqhpr gur EBG13 bs gur vachg. Nyy punenpgref orfvqrf N-M fubhyq or pbcvrq gb gur bhgchg ireongvz, naq pnfr fubhyq or cerfreirq vs cbffvoyr.

Nal ynathntr gung pna ernq naq jevgr fgnaqneq fgernzf vf snve tnzr.

Befunge - 7x30 = 210 6x26 = 156 characters

New streaming version that supports both upper and lower case and should support unlimited input.

v,<               <<     <
  ^-4-9<    >:"A"\`|
     >:"a"\`|     #>:"Z"`|
>~:0`| #    >:"z"`|
,    @ |    <`"m":<v`"M":<
^  +4+9<    ^      <

The old version

This stores the values inside its own source code. Really shows off how horrible it is to try and output stored values in the same order that you receive them. Only supports lowercase characters.

vp0p11:+1g11<      < <
v                    ^-4-9<
v    >:"a"\`|>:"z"`|>:"m"`|
>~:0`|      >^     >^#
                     ^+4+9<
     >$011g1+0p>12g1+:12p0g:v
               ^           ,_@

I'm not sure exactly what limitations this has, using http://www.quirkster.com/js/befunge.html as the interpreter it does appear to break with large inputs.

Python (117 bytes)

Here's a Python version that avoids the rot13()-method.

import sys
print"".join([chr(x/32*32+1+(x%32+12)%26if 64<x<91or 96<x<123 else x)for x in map(ord,sys.stdin.read())])

Bash - 5 chars

rot13

I've got 34 chars on python:

print raw_input().encode('rot13')

C - 83 79 characters

main(c,b){while((c=getchar())>=0)b=c&96,putchar(isalpha(c)?b+1+(c-b+12)%26:c);}

Readable version:

#include <ctype.h>
#include <stdio.h>

int main(void)
{
    int c, base;

    while ((c = getchar()) >= 0) {
        if (isalpha(c)) {
            base = (c & 96) + 1; /* First letter of the upper or lower case. */
            c = base + (c - base + 13) % 26;
        }
        putchar(c);
    }

    return 0;
}

tr/// solution in Perl (39 characters), boilerplate can be removed with -p:

while(<>){y/a-zA-Z/n-za-mN-ZA-M/;print}

Using -p (23 characters including the extra switch):

perl -pe'y/a-zA-Z/n-za-mN-ZA-M/'

DC (111 108 for the dc itself)

Ok, here it is in (mostly) dc and some sed and od magic to get it into the right format for the code. If you don't count the input thing (echo -n MESSAGE |) it's 160 bytes:

od -An -t dC|sed 's/^\ *//;s/\ \{2,3\}/\n/g'|dc -e'[13+26%]sm[65-lmx65+]su[97-lmx97+]sl[96<b64<dPc]sa[91>c]sd[123>e]sb[lux]sc[llxdd]se[ddddlaxlrx]sy[?z0<y]dsrx'

As a point of interest, the dc programme itself is only a 108 bytes long, shorter than the non-library python version. It even preserves case and punctuation, and beats Javascript in the above submission! If only I could better parse the output of od, or better yet replace it altogether.

EDIT: It's worth noting that the question doesn't indicate a trailing new line 10P which saves me three further bytes.

EDIT 2: There's no specification for the format of the input, so I assume it's taken in as is convenient for my programme :P

Perl6 (54)

$*IN.lines».trans("a..zA..Z"=>"n..za..mN..ZA..M").say

Haskell, 100 characters

a%b=([a..b]++)
main=interact$map$toEnum.((0%64$78%90$65%77$91%96$110%122$97%109$[123..])!!).fromEnum

Javascript (177)

This assumes that there are two functions, print and readLine:

f=String.fromCharCode;print(readLine().replace(/[a-z]/g,function(a){return f((a.charCodeAt(0)-84)%25+97);}).replace(/[A-Z]/g,function(a){return f((a.charCodeAt(0)-52)%25+65);}))

PHP - 41 Characters

while($r=fgets(STDIN))echo str_rot13($r);

PHP - 103 98 80 characters

(not using str_rot13())

<?=preg_replace('#[a-zA-Z]#e','chr(($x=ord("\0"))-$x%32+1+($x%32+12)%26)',`cat`);

Delphi, 110

var c:Char;begin repeat Read(c);Write(Chr(Ord(c)+(Ord(c in['A'..'M'])-Ord(c in['N'..'Z']))*13));until EOF;end.

Java 251 chars

public class r{public static void main(String[] a){String s = a[0];for(int i=0;i<s.length();){char c=s.charAt(i++);if(c>='a'&&c<='m')c+=13;else if(c>='n'&&c<='z')c-= 13;else if(c>='A'&&c<='M')c+=13;else if(c>='A'&&c <='Z')c-=13;System.out.print(c);}}}

Python 3 (107)

Ok, I promise to stop answering this question now, but I felt compelled to beat the DC answer in Python. This probably reflects poorly on me as a person :).

import sys;[print(x.isalpha()and chr((ord(x)&96)+1+(ord(x)%32+12)%26)or x,end='')for x in sys.stdin.read()]

Haskell - 112 characters

r l=drop 13 l++take 13 l
t=['a'..'z']
s=['A'..'Z']
main=interact$map(\x->maybe x id$lookup x$zip(t++s)$r t++r s)

JavaScript 1.8, 106

alert(prompt().replace(/\w/g,function(c)String.fromCharCode(c.charCodeAt()+(c.toLowerCase()<'n'?13:-13))))

JavaScript, 115

alert(prompt().replace(/\w/g,function(c){return String.fromCharCode(c.charCodeAt()+(c.toLowerCase()<'n'?13:-13))}))

This solution solves the problem by adding 13 to the character code if the character in question is in the first half of the alphabet, or subtracting 13 if it's in the second half.

C: 69 68 characters

Alright, I know this thread is long dead, but I couldn't stand the (long) C-solution which doesn't even compile on Clang (but does on GCC).

main(c){putchar(isalpha(c=getchar())*((c|32)<110?13:-13)+c);main();}

It is probably almost still squeezable. It certainly was squeezable. And not only was it squeezable, it was possible to make it recursive.

PHP – 18 characters

str_rot13('text');

Scala 108

def m(a:Int,z:Int,c:Int)=if(c>=a&&c<z)a+((c-a+13)%26)else c
"Ok?".map(c=>print(m(65,91,m(97,123,c)).toChar))

ungolfed:

def m (a: Int, z:Int, c:Int) = if (c >= a && c <= z) a+((c-a+13)%26) else c
"Ok?".foreach (c => print (m ('A', 'Z', m ('a', 'z', c)).toChar))

result:

Bx?

Mathematica 102

StringReplace[Input[],
Join@@Table[Rule@@FromCharacterCode/@{i+c,Mod[i+13,26]+c},{c,{65,97}},{i,0,25}]]

K, 31

{x^(,/{x!(13_x),13#x}'.Q`A`a)x}

Tcl, 74 chars

package require [set c tcl::transform::rot];$c 13 stdin;fcopy stdin stdout