I don't like to chase hogs and have had poor luck with heart/lung shots providing reliable stops. The hogs still die, but after running X distance, usually into the brush which is often briar and poison ivy. They never run to the truck. So head/CNS shots are my preferred shots.
As noted above, you can use a lot of rifle calibers, but the larger or more powerful the caliber, the more likely to produce a quick stop. Remember, it isn't just about placement, but also trajectory and penetration. You have to think of the hog as a three dimensional animal, not a two dimensional target. You aren't trying to hit a spot outside of the hog, but inside. Your aim outside of the hog should be determined by the hog's orientation to you relative to what is inside. It really doesn't matter where the entry is so long as the bullet penetrates sufficiently and hits the necessary structures to produce a proper kill.
It was pointed out where to aim on the shoulder. That is just fine if the hog is absolutely broadside to you. If the hog is quartered toward you, then you are going to want to aim forward of the shoulder so that as your shot traverses the body, it passes through the correct heart/lung structures. If quartered away, behind the shoulder. Just how far foward or behind will be determined by just how much the hog is quartered relative to you.
The last sow I shot was fairly severely quartered away. My shot was about mid body which would be a terrible broadside shot, but put the bullet through the liver and into the lower portion of the heart. She did run about 50 yards, into briar and poison ivy.
As for not standing still, if you have the hog at a destination location (feeding, drinking, resting/sleeping, etc.), the hog is going to get still for you. That can be good for a shot to the vitals or to the CNS structures of the head. Hogs on the move will often stop occasionally as well. Hogs may not remain still for long, so you need to be ready to shoot for when the hog does get still.
What I have noticed is that hogs will often do what I call "security checks." Individuals entering a clearing or traversing an wide area will often stop briefly, usually stand very still, often nose high (sampling air), and then continuing on once they feel safe. A loner or all the individuals in a small group may do this and sometimes do it at the same time. In bigger groups, some individuals will be vigilant and the rest will be oblivious. The vigilant ones are the ones stopping to check their surroundings and often make for the best target. Watch their behavior and usually you can spot patterns fairly quick. Some hogs make prolonged security checks and some make shorter ones. Watch your hog and be on target and ready when he makes his next stop.
Feeding hogs are great targets, especially with a concentrated resource such as a bait station, but also when rooting. They will remain stationary in a given location for longer periods of time when feeding and often their head will be fairly stationary as well.
Here are some videos showing what I am talking about. Note that most folks take head shots inside of 100 yards.
Feeding head shots...
http://www.youtube.com/watch?v=zgG7JWMa6gM
http://www.youtube.com/watch?v=YR9gnMHSkfw
http://www.youtube.com/watch?v=-Gmhg9OGhpg (this guy has some neat vids)
http://www.youtube.com/watch?v=kfPoRQomw5o (2:40 in video)
http://www.youtube.com/watch?v=Eq8RZbyyb1g (LOL, the pig "looked big through the scope")
http://www.youtube.com/watch?v=llw1aUJmjHQ
Feeding vitals shots...
http://www.youtube.com/watch?v=-94O8o0X-6s (note shot deflects out of hog and how far hog runs)
Security Checks, then feeding head shots...
http://www.youtube.com/watch?v=i6dv32qaQ6s (check little red hog at 1:42 doing security checks, sows (?) doing checks at 2:55...)
Feeding vital shot double bow kill...
http://www.thehighroad.org/newreply.php?do=newreply&noquote=1&p=8914378
Security check vitals bow shot ...
http://www.youtube.com/watch?v=xmLYNGDLqGs (0:40, then feeding @ 2:00)
You can do you own searches and see when folks are picking their shots, but as you can see, hogs are often still enough to make good head shots, but you need to be certain of your zero and if you take the head shot, plan it so that if you err, that your err is toward the neck and not toward the nose. With a good rifle caliber, you often get the necessary CNS damage via hydrostatic shock to the brain and/or brain stem.
Like I said, I do like head shots, but if they aren't for you, that is fine. You can use the same information about waiting for hogs to go still for making vitals shots.