I made coconut rice for the first time tonight and absolutely loved it. I used regular basmati rice (any other kind of white rice would have worked) and replaced the cooking water with coconut milk and a 1/4 teaspoon of salt. My preference is to cook with the light coconut milk, because the regular has so much fat in it.
As it cooked, the rice absorbed the coconut milk and got incredibly creamy. It did cook quicker when compared to cooking rice with just water (about 15 minutes total vs 20). I served it with a shrimp curry, and the flavors of the rice made it more than just a side dish. Give it a try!