Disclaimer: keep in mind that I'm a midwestern white boy who's never been closer to the Indian subcontinent than, say, Italy.
Kheer is (from what I can gather) a (reasonably close to) traditional Indian dessert. It can be prepared any number of different ways, and who am I to tell you which one is the best? Regardless, it can often be found in (United States of) American restaurants which purport to feed you "Indian food". I don't think that Indian restaurants in the States have gotten quite as bad as, say, "Chinese food" restaurants, with respect to inventing cuisine for stupid Americans who won't know any better, so I suppose that's OK. From what I've read on the web, it seems people from India really do eat this too, so I think I'm OK here. Feel free to correct me if I've done the equivalent of claiming that Sweet and Sour Chicken is a 'traditional Chinese dish...'
The five or so different places I've had kheer, it's been a thin, not-quite soupy consistency rice pudding of sorts. It has a distinctive flavor, which is very pleasant. Delicious, really. It sometimes comes with raisins or sliced almonds blended into it. I'm told it can be served warm or chilled. I highly recommend it. I've only ever had it chilled, though.
If you'd like to try to make some yourself, here's a recipe I've gratuitously yanked off the web while failing to properly credit the author. I've yet to make it, so no guarantee as to its a) accuracy, b) quality, c) authenticity, or d) fitness for human consumption.
Place milk in a large pot and begin to heat in order to bring to a boil. Ground the saffron strands and soak in warm milk. In the meantime, wash the rice well. In a small pan, heat 1 teaspoon of butter or ghee. Add the rice and sauté for 4-5 minutes (do not brown). This will strengthen the rice so that it will not break. Once the milk has reached a boil, add the rice.
Lower the heat and bring to a rolling boil. Boil for about 35-40 minutes, allowing the rice to cook. Add sugar, cardamom, saffron, almonds, and raisins. Cook for an additional 5-6 minutes. Use additional almond slivers, pistachios, fruits, etc. for garnishing.