Multiply without multiply

C, 84 83 78 Characters

m;main(a,b){for(scanf("%d%d",&a,&b);a;b+=b)a&1?m+=b:0,a>>=1;printf("%d\n",m);}

In a more readable form

m;main(a,b)
{
    scanf("%d%d",&a,&b);
    while (a)
    {
        if (a&1)
           m+=b;
        a>>=1;
        b+=b;
    }
    printf("%d\n",m);
}

The algorithm is better known as the Ethiopian Multiplication or the Russian Peasant Multiplication.Here’s the algorithm :

1. Let the two numbers to be multiplied be a and b.
2. If a is zero then break and print the result.
3. If a is odd then add b to the result.
4. Half a, Double b. Goto Step 2.

APL (5)

Takes input on standard input separated by newlines.

+/⎕⍴⎕

Golfscript - 12 characteres

~0\{1$+}*\;

Please note that * here is not the multiplication operator, it's instead a repetition operator, see the second use here.