Perl

The function CompareStrings takes any number of strings and returns the strings true or false:

• true is returned if there are one or more strings and all strings are equal.
• false is returned if there is no string or at least two different strings.

sub CompareStrings (@) {
    my %hash = map { $_ => 1 } @_;
    return ('false', 'true')[not scalar(keys %hash) - 1];
}

The strings are put as keys in a hash. If there is at least one string and all strings are equal, then the hash has one key exactly. Otherwise there are zero or two or more keys. After 1 is subtracted the operator not maps the cases to the empty string and 1 that are used to select the result string (the empty string becomes 0).

sub CompareStrings (@) {
    my %hash = map { $_ => 1 } @_;
    return ('false', 'true')[not scalar(keys %hash) - 1];
}

Complete script with test cases:

#!/usr/bin/env perl
use strict;
$^W=1;

sub CompareStrings (@) {
    # several variants to initialize the hash, whose keys are the strings:
    # my %hash; @hash{@_} = (1) x @_;
    # my %hash; $hash{$_} = 1 for @_;
    my %hash = map { $_ => 1 } @_;
    return ('false', 'true')[not scalar(keys %hash) - 1];
}

# Testing

$\ = "\n";
print CompareStrings qw[];                  # false
print CompareStrings qw[foobar];            # true
print CompareStrings qw[hello hello];       # true
print CompareStrings qw[Hello World];       # false
print CompareStrings qw[abc abc abc];       # true 
print CompareStrings qw[abc abc def];       # false
print CompareStrings qw[abc def ghi];       # false
print CompareStrings qw[a a a a a a a a];   # true
print CompareStrings qw]a a a a oops a a];  # false

__END__

GolfScript

1$=:a;=a+2="true""false"if

This program assumes three strings on the stack.

Test online

How it works:

1. 1$ copies the second element on the stack (the second string) to the top of the stack.
2. =:a; returns 1 if the two top elements (the second and the third string) are equal; otherwise, 0. Then, it stores this result in the variable a and it pops it from the stack. Now only the first and the second string remain on the stack.
3. = checks whether the first and the second string are equal.
4. a+ puts the value of a on the stack and calculates the sum of a and the result of the previous comparison.
5. 2="true""false"if puts "true" on the stack if the sum of the comparison results is equal to 2: in this case, both comparisons returned true. If the sum is 1 or 0 then it puts "false" on the stack. This value is now the only one on the stack, and at the and of a program, GolfScript always outputs the values on the stack.

[Edit]

Thanks to Peter Taylor for pointing out that variables are not necessary:

1$=@@=+2="true""false"if