Ruby, 105 110 142 114 characters
o=%w{+ - * /};[*ARGV.permutation].product(o.product o).map{|x,y|e=x.zip(y)*"";p"#{e}=#{eval(e)rescue:N}"}
Usage
ruby prog.rb 1 2 3
Explanation
# o = ["+", "-", "*", "/"]
o=%w{+ - * /};
# ARGV = array of numbers. Generate all permutations, and apply splat operator
[*ARGV.permutation]
# Generate cartesian product of all permuted numbers and operators
# There will be 16 operator permutations, and 6 number permutations giving a
# total of 96 elements
.product(o.product o)
# For each of the 96 pairs, merge the operators and numbers into 1 array.
# ex - [1,2,3].zip(["+", "-"]) gives [[1, '+'], [2, '-'], [3, nil]]
# then convert the array to string by multiplying with "" => "1+2-3"
.each{|x,y|e=x.zip(y)*"";
# print output and eval result. On exception return infinity - ∞
p"#{e}=#{eval(e)rescue:N}"}
Output
1+2+3=6
1+2-3=0
1+2*3=7
1+2/3=1
1-2+3=2
1-2-3=-4
1-2*3=-5
1-2/3=1
1*2+3=5
1*2-3=-1
1*2*3=6
1*2/3=0
1/2+3=3
1/2-3=-3
1/2*3=0
1/2/3=0
1+3+2=6
1+3-2=2
1+3*2=7
1+3/2=2
1-3+2=0
1-3-2=-4
1-3*2=-5
1-3/2=0
1*3+2=5
1*3-2=1
1*3*2=6
1*3/2=1
1/3+2=2
1/3-2=-2
1/3*2=0
1/3/2=0
2+1+3=6
2+1-3=0
2+1*3=5
2+1/3=2
2-1+3=4
2-1-3=-2
2-1*3=-1
2-1/3=2
2*1+3=5
2*1-3=-1
2*1*3=6
2*1/3=0
2/1+3=5
2/1-3=-1
2/1*3=6
2/1/3=0
2+3+1=6
2+3-1=4
2+3*1=5
2+3/1=5
2-3+1=0
2-3-1=-2
2-3*1=-1
2-3/1=-1
2*3+1=7
2*3-1=5
2*3*1=6
2*3/1=6
2/3+1=1
2/3-1=-1
2/3*1=0
2/3/1=0
3+1+2=6
3+1-2=2
3+1*2=5
3+1/2=3
3-1+2=4
3-1-2=0
3-1*2=1
3-1/2=3
3*1+2=5
3*1-2=1
3*1*2=6
3*1/2=1
3/1+2=5
3/1-2=1
3/1*2=6
3/1/2=1
3+2+1=6
3+2-1=4
3+2*1=5
3+2/1=5
3-2+1=2
3-2-1=0
3-2*1=1
3-2/1=1
3*2+1=7
3*2-1=5
3*2*1=6
3*2/1=6
3/2+1=2
3/2-1=0
3/2*1=1
3/2/1=1
