I see humbuckers, single coil, active pickups, etc. I see P90's, PAFS, etc. Which are basically for jazz, blues, metal?
Well, it's a tough call; There's no set "rule" but i'll try and give you the lowdown on the "common" or stereotypical use of each pickup.
First let's talk about active pickups. Generally active pickups can get higher output and, due to that fact, they're a pretty popular choice for metal players. The most popular active pickups are EMGs. You'll see EMG 81's are a very popular bridge pickup for metal and EMG 85's are super popular for the neck (that's the Zakk Wylde combo). The 60 is popular too (James Hetfield uses those).
At the opposite end of the spectrum you see Steve Lukather from Toto uses EMGs in his guitars. He's known for rock, jazz, fusion and blues. So, active pickups aren't necessarily for metal, but they're popular with metal players.
Lots of folks claim active pickups sound sterile. Its all opinion.
OK single coils:
Single coils are the kind you'll see on Strats. They're very popular all around but are quite prolific in rock, surf music & blues (think SRV). A single coil at the bridge w/ some overdrive gives you that nice dirty blues type of tone.
But, then again, strats have been used by many, many folks for many varieties of music. One example is Pete Townsend: he's used and is currently using strats. So, again, you cannot pigeon-hole the pickup to a specific style of music. Also, Ritchie Blackmore from Deep Purple played a star a lot too.
One thing to keep in mind with the single coils is that they're often on strat-style guitars that have 3 pickups. With a 5 way switch you get the quacky tones w/ the in-between positions (combine neck or bridge pickup w/ the middle one). This combination of the 2 single coils is a very distinct tone & something you can't easily achieve w/ another pickup combination.
Tele style single coils are different than your strat style single coils and are well known for "twang". Think twangy country music.
P90s are single coil pickups. However they're hotter than the strat style single coils and have a less "crisp" tone. They can sound nice and mean too. The Les Paul Junior, in my opinion, is "the" P90 guitar.
P90's are pretty diverse and can be heard all over the last few Green Day albums. They're also the pickups George Thorogood has on his guitar - so they're great for blues as well as the Green Day style punk rock. They're great for country too. Check out http://www.youtube.com/watch?v=OSSjYFPTRAQ for an example.
OK... now off to humbuckers & PAFs. PAFs are the first humbucker pickups. PAF actually stands for Patent Applied For. Nowadays PAF designates a "class" of humbuckers.
Humbuckers come in 2 major varieties: high gain (things like the Duncan JB or a Dimarzio Super Distortion) & PAFs which denotes the not-super-high-gain type humbuckers.
Humbuckers don't hum like single coils do. Single coils have a 60 cycle hum to them. When you join 2 coils that hum is cancelled... or bucked =)
Like the other types on pickups you can't just say "humbuckers are used for x". They're used for many genres; from BB King to Slash to John Petriccui. All the way from blues to drop-tuned metal.
They've definitely got more body than both single coils and p90s. If you really, really want screaming pinch harmonics, you'll want a humbucker. If you want sweet, smooth & creamy tone you'll also want a humbucker w/ the tone knob cracked all the way down to 0.