Generate A Weighted Random Number

Rejection sampling (such as in your solution) is the first thing that comes to mind, whereby you build a lookup table with elements populated by their weight distribution, then pick a random location in the table and return it. As an implementation choice, I would make a higher order function which takes a spec and returns a function which returns values based on the distribution in the spec, this way you avoid having to build the table for each call. The downsides are that the algorithmic performance of building the table is linear by the number of items and there could potentially be a lot of memory usage for large specs (or those with members with very small or precise weights, e.g. {0:0.99999, 1:0.00001}). The upside is that picking a value has constant time, which might be desirable if performance is critical. In JavaScript:

function weightedRand(spec) {
  var i, j, table=[];
  for (i in spec) {
    // The constant 10 below should be computed based on the
    // weights in the spec for a correct and optimal table size.
    // E.g. the spec {0:0.999, 1:0.001} will break this impl.
    for (j=0; j<spec[i]*10; j++) {
      table.push(i);
    }
  }
  return function() {
    return table[Math.floor(Math.random() * table.length)];
  }
}
var rand012 = weightedRand({0:0.8, 1:0.1, 2:0.1});
rand012(); // random in distribution...

Another strategy is to pick a random number in [0,1) and iterate over the weight specification summing the weights, if the random number is less than the sum then return the associated value. Of course, this assumes that the weights sum to one. This solution has no up-front costs but has average algorithmic performance linear by the number of entries in the spec. For example, in JavaScript:

function weightedRand2(spec) {
  var i, sum=0, r=Math.random();
  for (i in spec) {
    sum += spec[i];
    if (r <= sum) return i;
  }
}
weightedRand2({0:0.8, 1:0.1, 2:0.1}); // random in distribution...