There are now over 25 different types of rice available, with several new hybrids. In general, short- and medium-grain rices work well for rice puddings, since the starch in them breaks down and helps to thicken the pudding. Long-grain rice can also be used for rice pudding, if you cook it enough.
Experiment with other rices—basmati and Texmati add surprising flavor. Both wild rice (not a true rice) and brown rice also make delicious puddings (see the recipes on).