[Another Update:] Check out the Onigiri FAQ  for answers to most, if not all, your onigiri related questions!
[One more Update:] A few people are obviously not taking the time to read or follow the links suggested properly. Otherwise they would not keep asking the same question, or worse answering it wrong, over and over. So please let me repeat again:
The best rice to use for standard onigiri is the kind usually sold as Japanese rice or 'sushi rice'. It is NOT THE SAME as 'sticky rice' or 'sweet rice' or 'glutinous rice'. And no you cannot use jasmine rice for successful onigiri, the way onigiri are supposed to be! The right kind of rice, properly cooked, is not the same as the wrong kind of rice, cooked until mushy and pressed together in a gluey fashion. If you can't get a hold of Japanese rice for some reason, there are a few other rices that can be substituted. See Looking At Rice  for a complete explanation. That should make things clear! (end Update)
One of the most popular entries on this site is the one about onigiri , or Japanese rice balls, which I wrote back in 2003. (A lot of people landed there searching for onigiri as portrayed in anime or manga, especially Fruits Basket ...which is interesting.) It was one of the very early entries on the blog, and I gave the traditional way of making the onigiri: hot rice put on moistened and salted palms, which quickly turn red and sore because of the heat from the rice.
I've made hundreds of onigiri in the 3 years since I wrote that, because onigiri are such great portable meals for picnics, not to mention party food and late-night snacks. But let's face it, those red sore palms aren't too pleasant, and the rice grains do tend to stick all over the place. Also, portioning with the rice scooper can be a bit erratic unless you are an onigiri-making expert.
With ideas from several places including cookbooks, Japanese TV shows and my mother, this much neater method of making onigiri evolved. It requires no special molds or equipment. It ensures that all your onigiri are uniform in size. Your hands never get too hot and red. And, if you're going to bring them on a picnic or store them for eating a bit later, they're already conveniently pre-wrapped in plastic.
A word here from my mom about the most frequently asked question regarding onigiri: alternative fillings if you can't get a hold of, or don't like, the traditional fillings like umeboshi (pickled plums), tarako (salted cod roe), or katsuobushi (bonito flakes) with soy sauce. She says, "Onigiri isn't about the filling really. It's about enjoying the flavor of good rice." She has a point there. Use good rice, prepared properly, and the filling becomes secondary.
So, I present you... Onigiri 2.0 :).
There are a lot of steps here, but once you have done a couple this way you will be turning out tons of rice balls in no time.
Equipment and ingredients needed:
Covers of your choice such as nori seaweed
Mise en place: Make ready your teacup, a cup or bowl holding some water, salt shaker, rice, rice scoooper, fillings, plate to put the finished onigiri, and plastic wrap roll. It's easiest to do this near the sink, if you have the space.
If you're going to bring the onigiri on a picnic, just leave it in the plastic wrap, and bring along the nori separately; wrap the onigiri with the crisp nori just as you're going to eat it. If you're going to eat the onigiri right away, you can re-use the piece of plastic wrap for all the onigiri balls you make.
This method works marvelously for brown rice balls as well as white rice balls. Brown rice balls can be a bit tricky, since brown rice is not as sticky as white.
A lot of people ask about alternative fillings for onigiri. Basically anything that goes well with rice, is not too wet or oily, and is highly seasoned (read: quite salty) will work. There are several listed in the original onigiri article  as well as in the comments. Remember that any filling you use must be well cooked. Here are some that have been successful for me to varying degrees:
Remember also that you can have plain onigiri, flavored only with salt, to bring along as the carb component of a portable obento lunch or picnic, to eat with other things like chicken wings, boiled eggs, little meatballs on a stick, or whatever strikes your fancy.
The rather burned looking onigiri on the top right in the photo above is a yaki onigiri, or toasted onigiri, made of brown rice (genmai). It's actually 'toasted' in a hot dry non-stick frying pan until the surface rice grains get brown and toasty, then brushed on both sides with soy sauce. This is a great way to revive onigiri that's gone a bit dry on the outside. You can put a little bit of sesame oil in the pan to add even more flavor. Brown rice onigiri is especially good as yaki onigiri, since the toasting really brings out the nutty flavor. You can also toast the onigiri in a toaster oven; toast first, then brush with soy sauce, and toast a bit more until your house smells like a giant rice cracker.
(A word of clarification here: What makes this method a little different is the use of both the cup and the plastic wrap: the cup helps you produce uniformly sized onigiri, which can be an issue for onigiri neophytes, and the plastic helps to avoid the red, sore hands. It's meant to be very beginner friendly. If you or your mother/aunt/wife/friend already uses a similar method, terrific! That's just confirmation that it works, isn't it? And, if you/your mother/etc. can whip out tons of onigiri without resorting to 'gimmicks', all the more power to you. )
Before asking a general question about onigiri, please check out the Onigiri FAQ page . Chances are your answer is already there!
Update, September 2009: I am closing comments here, since the same questions keep getting asked over and over. Maybe there are too many comments for people to read through. Most if not all your onigiri questions are answered in the Onigiri FAQ . If they are still not answered, then ask your question over there. Thanks!