Not sure how much rice you are making, but if making about 2 cups of rice, first heat 3 tablespoons of peanut oil over Medium High heat.
Add the rice and toast it in the oil until it releases a nutty fragrance - about 1-2 minutes.
Then I like to use Chicken stock (3 cups) to finish it off.
Personal preference
but I like to add scallions (green onions) and cilantro to the rice when it is done.
Cooking it this way I have not noticed a tremendous taste difference from different brands of Jasmine Rice.
cooking.stackexchange.com/users/6817/allnet000
A few things come to mind: Before cooking: Cook the rice in coconut milk, maybe with a piece of ginger or Put a teaspoon or two of cumin seeds in the cooking water After cooking: Mix with fried scallions, ginger and mustard or cumin seeds
cooking.stackexchange.com/users/6531/nico
Jasmine is specific as it has high GI index.
As for the flavor, it is a bit bland on top, but should have a floral fragrance, so it is perfect for Thai, Indonesian, Malay and other far east recipes where you have very strong sauces or tastes from the main dish (where basmati would be best for Indian and middle eastern dishes).
NOTE:
I would not call myself a cook, but my Thai friend, whom I would, used to use a mix of three types of rice, some for texture and some for taste (SEA dishes).
Also, I must say that I got aware of subtleties in taste of rice only after few months of heavy rice diet.
cooking.stackexchange.com/users/6783/Unreason
Although I have not tried this with jasmine rice, I think you can try cooking it like the Indian pulao .
In a tbsp or two of neutral vegetable oil fry 2-3 cloves, 1-2 inches of cinnamon, and 4-5 whole cardamom pods.
When spices release their flavor, add jasmine rice soaked for roughly half hour and drained.
Fry the rice for a couple of minutes and then cook it in water, as you would usually do.
The aromatic spices will impart a nice flavor to the rice.
Alternatively, you can also add star anise or fried onion.
cooking.stackexchange.com/users/4817/Avinash Bhat
In my experience, it at least partly depends on where you buy your jasmine rice.
If you buy it at a large American grocery store chain, you'll get something bland.
I don't know where they get it or what they do to it, but it has no smell or flavor.
If you buy it at a small Asian grocery, it will taste and smell very good, and complement the dishes you serve it with.
cooking.stackexchange.com/users/6512/thursdaysgeek
Replace your rice water with stock.
Vegetarian/vegan?
Use vegetable stock instead.
Other liquids to intensify the flavor--
rice wine, rice vinegar, soy sauce.
I'm sure you could use the Western style wines/vinegars too, though I haven't tried with those specifically.
allnet's answers cover the rest of what I would say: basically toasting the rice and using herbs/spices.
cooking.stackexchange.com/users/6818/Eric Hu
What I ended up doing, which worked well: Toast rice before cooking until just a hint of golden brown appears, and a nutty smell is produced (as per allnet's and avinash's suggestions, which is why allnet's answer was accepted) Add minced garlic and diced Roma tomato to rice just before toasting is done (for 2 cups dry rice, I used 3 cloves garlic, 1 medium Roma)
Add caramelized onions both before and after cooking rice.
This is similar to the "fried onions" suggestion. Add an additional diced tomato after rice is cooked Finish flavor of cooked rice with rice wine vinegar, honey, and a touch of lime juice
My girlfriend called the final result the best of my cooking experiments, after chicken breaded with pakora batter.
Thank you everyone that had suggestions!
I think toasting the rice made the biggest difference from previous versions.
The rice released a very delicious flavor and smell.
I could have used even more onion and garlic; although I thought the amount excessive based on the smell when cooking, the actual flavor was fairly mild afterward.
I will experiment with adding toasted cumin, mustard seeds, and ginger to my current result.
Don't have good (read: homemade not crappy grocery store) stock or scallions to play with right now.
cooking.stackexchange.com/users/6345/BobMcGee
Tilda Rice & Spice guide suggests jasmine rise teams perfectly with ginger, lemongrass, galangal, lime, green chilli and kaffir lime leaves.
So maybe try ginger instead of star anise, which is a better match for basmati.
cooking.stackexchange.com/users/83376/Slightly Later Man
I'm used to cooking basmati, which can stand on its own with just a few spices and a little butter.  With jasmine rice, I come away disappointed; the rice never seems to bring anything to the dish, and generally comes off a little bland, even with fairly potent flavorings.  Is there some technique or trick specific to jasmine rice that I should be using?  Are there particularly good flavor/ingredient combos for jasmine rice I can use?
How can I get more flavorful jasmine rice?
cooking.stackexchange.com
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cooking.stackexchange.com/questions/16296
cooking.stackexchange.com/users/6345/BobMcGee
Try cooking it with stock or coconut milk rather than water, maybe adding ginger to the coconut milk. Tilda Rice & Spice guide suggests jasmine rise teams perfectly with ginger, lemongrass, galangal, lime, green chilli and kaffir lime leaves, which can often be added after cooking. You could also cook it like Indian pulao. The taste can also depend on the source of the rice. Cook in stock instead of water and think about adding spices and flavourings.
Cook in stock instead of water. Add scallions, cook in coconut milk, add ginger, lemongrass and green chili. Try cooking in a pulao style. It depends where you buy your rice.