I can only answer from a perspective of the Indonesian kitchen, and my own personal experience, but in general the answer is:
In the water, with the rice
I quite often use saffron, turmeric, cloves, daun salam (The English Wiki entry links to bay leaf, which, completely, utterly, is not the same thing), and lemongrass, and they all go in while cooking the rice.
Possible exceptions would be green leafy herbs, (coriander / cilantro for instance), which you put in the end. Not so much to flavor the rice, but more to "scent" the bowl of rice.
In answer to your edit:
There is no preferred way. The preferred way depends on the herb, as observed by thrig in his/her answer. Going by experience, and the herbs I use myself, the answer is in the water with the rice. Putting a bay leaf in after the fact, is not going to do much for a dish. Putting it in while cooking the dish is. This goes for a lot of herbs: Turmeric, ginger and laos (galangal?) can flavor rice, but not if you put it in the end. On the other hand: Putting cilantro while cooking the rice will just destroy the cilantro, and leave nothing to show for it. I lack the knowledge of what is water-soluble, and what is fat-soluble, but as a general guideline I use my highly personal "is-this-going-to-survive-the-15-to-20-minute-cooking-process-or-not?" guideline, and the even more personal "did-it-work?" guideline.
In addition, and perhaps also supporting thrig's answer, Indonesians are not shy of cooking their rice in santen (again: English wiki does not do justice, creamed coconut is not quite the same), adding a mildy greasy layer to the grains, aiding in flavor absorption, although I have to say it's not a common practice, but more often used for festive occasions.