C <del>924</del> <del>882</del> <del>622</del> <del>603</del> <del>587</del> 569 chars
=

With obvious newlines removed (retained for readability).

    #define A sbrk(8);signal(11,S);
    #define W(x)write(1,x,1);
    #define P (t>s?*--t:0)
    #define U *t++
    #define B(x,y)else if(b==(w=w+1 x)){w=P;y;U=w;}
    *t,*s,w,a,c,d;char b;S(x){A}
    p(x){if(x<0){W("-")x=-x;}if(x>9)p(x/10);b=48+x%10;W(&b)}
    main(){t=s=A U=0;
    while(read(0,&b,1)){w=47;if(0);
    B(,w+=P*pow(10,w?ceil(log10(w)):1))
    B(,++w)
    B(,--w)
    B(,w*=P)
    B(,w=P/w)
    B(,w+=P)
    B(,w=P-w)
    B(,w=pow(P,w))
    B(,w=P%w)
    B(,*t=w;w=*s;memmove(s,s+1,t-s<<2))
    B(+7,memmove(s+1,s,t++-s<<2);*s=w;w=P)
    B(,U=w)
    B(,a=P;U=a;U=w;U=a)
    B(,a=P;U=w;w=a)
    B(,a=P;c=P;d=P;U=a;U=w;U=c;w=d)
    B(,w=P)}
    for(W("[")t>s;)p(P),W(" ")
    W("]")}

This implements the "underflow pushes zero" interpretation from Jan Dvorak's comment.

Ungolfed:

    #include<math.h>
    #include<signal.h>
    void S(int x){signal(SIGSEGV,S);sbrk(8*8*8);}
    int*s,*t,*i,w,a,c,d;    //stack top index working accumulator count data
    u(x){*t++=x;}           //push()
    o(){return t>s?*--t:0;} //pop()
    p(x){                   //print()
        if(x<0){    //negative?
            W(*"-") //output '-'
            x=-x;   //negate
        }
        if(x>9)     //more than one digit?
            p(x/10); //recurse after integer-divide
        b=48+x%10;   //isolate and convert single digit to ascii
        W(b)         //output ascii digit
    }
    main(){
        char b[1];
        signal(SIGSEGV,S);  //auto-allocate memory for stack
        t=s=sbrk(8*8*8);  //get start of memory and allocate
        while(read(0,b,1)){
            write(1,b,1); //for debugging: echo the command being executed
            switch(*b){
                case '0': w=o(); a=o(); for(c=ceil(log10(w));c>0;c--) a*=10; u(a+w); break;
                case '1': u(o()+1); break;
                case '2': u(o()-1); break;
                case '3': w=o(); u(o()*w); break;
                case '4': w=o(); u(o()/w); break;
                case '5': u(o()+o()); break;
                case '6': w=o(); u(o()-w); break;
                case '7': c=o();a=1; for(w=o();c>0;c--) a*=w; u(a); break;
                case '8': w=o(); u(o()%w); break;
                case '9': w=*s; memmove(s,s+1,4*(t-s-1)); t[-1]=w; break;
                case 'A': w=t[-1]; memmove(s+1,s,4*(t-s-1)); *s=w; break;
                case 'B': w=o(); u(w); u(w); break;
                case 'C': w=o(); a=o(); u(a); u(w); u(a); u(w); break;
                case 'D': w=o(); a=o(); u(w); u(a); break;
                case 'E': w=o(); a=o(); c=o(); d=o(); u(a); u(w); u(d); u(c); break;
                case 'F': o(); break;
            }
        }
        write(1,"\n[",2);   //dump the stack
        i=t;
        do {
            p(*--i);
        } while(i>s && write(1,",",1));
        write(1,"]\n",2);
    }