I just finished installing a new pickup in my guitar and it does this weird thing, which had happened before too

The amp will make a humming noise but it changes in intensity as I turn to face the amp or face away from the amp. It seems to be the loudest when I'm facing it directly or when I'm not facing it directly, and it's barely there when the amp is to my side.
Other things could also cause humming noises. My CRT monitor makes my pickups hum so if you have a computer nearby. Many things can cause problems. Fan's can cause humming and lawnmowers nearby can be really bad because of the charged spinning blades.
Do you use a BR-600?
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yeah if i have my computer near my guitar while im playing it, or even my ipod on near my guitar, then itll have a weird humming noise. sometimes a TV does it
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i just finished installing new pickups, and anytime i touch the hardware or strings it hums, but otherwise it is one of the quietest guitars i've ever heard. everything is properly grounded according to the instructions as well...any ideas anyone? for some reason i was thinking black electrical tape on the amp output jack or having the main ground wire wrapped around a screw drilled into the side of the guitar near the springs(instead of soldered to the spring "claw") might help.
That happened to me once. Turned out I wired the hot and ground backwards on the jack. Try switching them and see if that helps.
HorsemanOfDeath, What hardware parts are you touching that causes a louder hum noise?

Typically you want to ground all your hard ware from the pickups shield to strings to pots to switches to the output ground.

Another way of reducing hum is using some copper foil sheets cut and glued into an empty electronics cavity. (Mine has adhesive on one side, so no glue needed)

Ultimately using pickups that cancel hum well whether stacked single coil or full sized humbuckers, this is achieved by having matched coils and many humbuckers have unmatched coils = more 60 Hz hum.