Any kind of pickup can be used for any kind of music, really, but there tend to be some trends--
*PAF-style (low-mid output) humbuckers are used for classic rock, blues, and jazz
*High-output humbuckers are favoured for hard rock and metal
*P90 single-coils are prominent in dirty rock and blues; rarely used for metal or hard rock. Some Jazz boxes use P90s, too. (incidentally, they're my favourites)
*Strat-style single coils are used for all kinds of rock, blues, R&B, or what-not. Not used too much these day in metal, though metal-players have certainly used them. Strats and teles (which also use single-coils) figure prominently in country music, too.
*Lipstick-tube single-coils are very low-output, making them quite suitable to clean applications like surf guitar or jangly pop
*Filtertron humbuckers are used a lot for rockabilly and country, though that seems to be more of an image thing than an actual sound-related thing since they are a Gretch pickup
*Mini-humbuckers are considered good pickups for blues and jazz
That list is by no means extensive, and it's a personal observation rather than a 'community-standard' factoid, though I'm sure many would agree with that assessment.
Greg