I think a recursive solution would be good for this one. So something like:

def PossibleWords(numberInput, cumulative, results):
    if len(numberInput) == 0:
        results.append(cumulative)
    else:
        num = numberInput[0]
        rest = numberInput[1:]
        possibilities = mapping[num]
        if len(possibilities) == 0:
            PossibleWords(rest, cumulative, results)
        else:
            for p in possibilities:
                PossibleWords(rest, cumulative + p, results)

result = []
PossibleWords( 1243543 ,   , result)

No need to go recursive. Here is an example of an iterative approach to start with. It prints out all the possibilities, but you may not entirely like its behaviour. The catch is left for the reader to discover ;-)

string tab[10]={"","","abc","def","ghi","jkl","mno","pqrs","tuv","wxyz"};
string s="1201075384"; //input string

for(int mask=0;mask<1048576;mask++)//4^10, trying all the posibilities
{
  int m=mask;
  string cur="";
  for(int i=0;i<s.size();i++,m/=4)  
    if (m%4<tab[s[i]- 0 ].size())
      cur+=tab[s[i]- 0 ][m%4];
  cout<<cur<<endl;
}

A C++ version of Smashery s python solution:

string getMapping(int num){
    assert(num>=2 && num<=9);

    switch(num){
        case 2:
            return "ABC";
        case 3:
            return "DEF";
        case 4:
            return "GHI";
        case 5:
            return "JKL";
        case 6:
            return "MNO";
        case 7:
            return "PRS";
        case 8:
            return "TUV";
        case 9:
            return "WXY";
        default:
            return " ";
    }
}


// Recursive function
void generateWords(string input, string cumulative, vector<string> &result){

    if(input.length() == 0){
        result.push_back(cumulative);
    }
    else{
        int num = input.at(0) -  0 ;
        string rest = input.substr(1, input.length()-1);
        string mapString = getMapping(num);
        if(mapString.compare(" ") != 0){
            for(int i=0; i<mapString.length(); i++){
                generateWords(rest, cumulative+mapString.at(i), result);
            }
        }
        else{
            assert(1==0);
        }
    }
}


void process(){

    generateWords("4734", "", words);

}