Since lead shot was outlawed for waterfowl hunting in North America in 1991, the varieties of alternatives have been growing.
Steel shot was the first to appear but steel has low density (hits softer, travels shorter, and thus requires larger shot size than lead). Many folks were reluctant to put magnum steel loads through older or valuable shotguns, it altered choke functioning, and many felt that steel produced too many crippled birds. (I thought so, but I am usually not a very good shot with waterfowl unless I am in the groove.)
Then came Bismuth, and Bismuth-Tungsten - all much more expensive than steel, but with densities closer to those of lead, and presumably gentler on the barrel than steel. Plus you use the same shot sizes as with lead, say, #4 for decoying ducks and BB for geese.
Here's a good brief summary: Shot-Buyer's Guide.
The non-toxic shot I've been hearing about lately is Hevi-Steel, an iron-tungsten shot which is as cheap as regular steel but with a density approaching that of lead. There's a good, detailed review of Hevi-steel here. Given the price, it sounds like an excellent choice for those giant flocks of Snow Geese.
You can compare non-toxic shot here at the Cabela's site.
I think Bismuth is my first choice for ducks, especially since I can do everything the same way I used to do with lead, but I wonder what our readers like to use for ducks and geese because I am no expert on this.