The question is not whether it is possible to wipe out a considerable part of the world population, but how long it will take before someone will find it worthwhile to even try it.
Apart from the insane points of view of religious and/or ideologic fanatics that have often been depicted in cheap novels and unrealistic B-movies throughout recent history there isn't a sane reason why anyone would want to kill each and every living soul on this planet.
Why? Earth would become a very harsh place to begin with, without all the complex chains of industry that are needed to provide even simple things like our daily bread, but even more importantly (and, suicidal fanatics, pay attention here) there's nobody left to appreciate the hard work that has gone into it. So there is no good reason to try it. But it might occur to someone that - while killing everybody isn't that smart - killing only half or at least a few billion of everyone would be a lot less stupid. Most of the machinations driving the world would still continue to churn on, and a lot of people would remain to appreciate, or at least remember in a very profound way, what happened.
So let's settle on three billion people. What would that bring us? What would be a decent reason to get rid of half your family, your town, your coworkers, etcetera?
Well, money and power of course. How would it feel to blackmail half of the world into oblivion and own the other half after the fact? Ethics aside, it might appeal to a very small fraction of mankind. And alas, a very small fraction is enough, being with 6 (almost 7) billion people in total. What would knowing that you will survive the next couple of years be worth to you? What price would you put on being certain that you and your loved ones would survive an approaching global disaster? Anything you have? Good. Now multiply that by three billion an you know what's at stake. The question how to collect all that wealth is something else entirely, but we will come to that.
So let's get working. The easiest way to kill a lot of people would be to throw something unhealthy into the air or into the water. All people need water and air all the time. It is not that hard to poison or pollute some small bodies of water unnoticed and history teaches us that many have once succeeded in doing so. We could choose to poison the world puddle by puddle, but this might be detected before we ever really get the hang of it. Timing is very important, because we don't want to spill the beans too early.
On a global scale however, this would mean an unpractical and expensive logistic nightmare. Expensive because of the necessary involvement of a lot of co-conspirators and the massive quantities of poison one would need to make or purchase and deliver. Unpractical because even one mistimed word of one of your partners in crime might put an untimely end to your dark plans.
Back to the drawing board. First problem: the enormous amount of unhealthy stuff we need to effectively kill 3 billion people. Three billion is a lot. To even feed each of them one teaspoon of whatever you fancy to do the trick, you would need 15.000 tonnes of it. Though this conveniently equals the cargo capacity of a Typhoon class Russian submarine, and thus also provide us with a stealthy delivery mechanism, it might be hard to maneuver such a monster through small rivers to reach even the remotest of people. If you had access to the distribution of drinking water, you would even need a lot more, because only a tiny fraction of that water actually is being drunk.
Luckily, there are poisons of which you'd only need a few nanograms per capita. This would lessen the transportation burden considerably, but we would still need the same distribution network to get it where you want it at the time you need it. That is, is we take it as a given that the chemical has to be produced in advance. But even this is not quite necessary.
We can make our own little portable production facilities instead. And even better, they can reproduce, so we wouldn't need a lot of it to begin with. The most toxic chemical in the world, botulin (also know for its application in cosmetic surgery under the alias Botox), is manufactured by a nice little bacterium. So people would not only die from it, they would also look good afterward. The only real problem is, we don't need it right away, but all at a certain moment in time. Can we pull that off? Yes we can. It is possible to let the gene that takes care of the botulin production express itself after a certain amount of generations. This can be programmed uncannily well if you know how to do it.
At this moment science hasn't progressed enough to postpone expression for more than two generations without bringing external stimuli to the game. You are undoubtedly familiar with the common wisdom that some treats skip one generation. This effect should be stretched to skip a lot more generations (and bacterial generations are short, mind you!). But a little more tinkering might very well enable us to time the manifestion of this property years into the future. The nice thing about it is that the bacteria can take their time to spread themselves all over the world without anybody knowing until it's much too late. And they aren't that hard to feed and keep alive.