I've a few. I've spent far, far too much money on pickups over the years but in doing so I've managed to come up with a very focused idea of what makes a fully responsive and dynamic pickup, so now I've got my selection pretty tight and down to just the same handful for every guitar.
#1 good-for-everything, default pickup: EMG 60AX. Note the 'A' and 'X', which for some reason most people completely overlook. This is not the 60 and most certainly nothing like the 81 and 85 which are all many people are familiar with. The '60' is the winding, the 'A' is a different magnet and the 'X' is a different preamp. Basically, it's a very low-wound humbucker with incredibly mismatched coils, with a flat preamp to get the signal back up to usable levels and, of course, the full sealing and noiseless operation of an active unit. It sounds a lot like a Firebird pickup, only a bit more 'open' because the coils are so underwound and unbalanced. People who say active pickups are bad, are less dynamic than passives or have—God forbid their English skills are this poor—"less tone" than passive designs have very obviously never tried the 60AX. Perfect as both a neck and bridge pickup.
The only way the 60AX is improved is by switching the horrible A5 magnet for an A4 one. This isn't a standard option and is not a modification you can do yourself, but if you ask EMG very, very nicely and happen to be a regular direct customer of theirs, they might knock you up a set. I do like the standard A5 60AX—it's one of only two pickups which make an A5 magnet sound acceptable—but the A4 is an inarguable improvement for general-purpose needs.
#2 good for-almost-everything, default pickup #2: Gibson BurstBucker #3. For my money, the best PAF-esque humbucker on the market. Gibson really got the coil balance just right with the BB#3. The #2 is good, too, though the #1 is rather poor. I've tried nearly every brand you can name, from big companies, small makers and the ''top'' boutique names, and the BB#3 is still the best PAF pickup I've heard. Hell, I've played with actual original PAF humbuckers and if given the choice, I'd still stick with the BB#3. The only drawback with the BBs is they are the most height-sensitive pickups I've ever found and they quickly become inaudibly thin or a muddy mess if you move them just a fraction of a millimetre too low or high. They can sound real bad if you don't get the height exactly right. Perfect as a bridge pickup, pretty good as a neck pickup although the #2 may be slightly better there depending on how much neck output you want.
#3 personal favourite for my particular style: Seymour Duncan Full Shred set with A4 or A8 magnets. I use these in a couple of Les Pauls with the tone controls disconnected completely. Much greater string separation than any other pickup with bar magnets, but still smoother than a pickup with pole piece magnets. The only problem is the horrific A5 magnet they come with as standard. One of my sets has A4 magnets instead and the other guitar has A8s. The tone between A4 and A8 isn't that different, it's mostly just a question of how well it handles low tunings before the 6th string becomes a muddy mess. I use the calibrated neck and bridge models in their respective positions. As a bonus, if you order directly from Seymour Duncan you can get metal covers as a shop floor mod but with the normal black hex poles showing through, which is a look I absolutely love.
Honourable mentions:
DiMarzio EVO 2: it's a Full Shred but with a more annoying magnet structure. At least it comes in purple, though. Bridge only, shit in the neck.
Seymour Duncan & Fender Pearly Gates Plus: kind of like a non-active 60AX. Still has the usual A5 problem of being on a nasal side, but it does better than any other passive A5 pickup. Makes a good neck pickup other than the pole spacing; a touch weak for the bridge.
Creamery humbucker-size P-90 with A4 magnets: the best hum-size P-90 without exception. It is indistinguishable from a standard P-90 pickup. Good for either position.
Swineshead AMP: the best use of pole piece magnets in a humbucker for proper single coil split tones and Wide Range-esque humbucker tones. Shame that the cockend behind Bare Knuckle drove them out of business with slander. Best at the neck.
Fender Vintage Noiseless Tele: Does what it says on the tin. Take your standard Tele bridge tone, lose the hum and shave the worst harshness from the treble end. Not a fan of the neck equivalent, but for a Tele bridge pickup there's nowt better.
EMG SAV: The only humless single coils worth a shit. Basically a 60s-style single coil with no hum and just a tiny, tiny bit more output so you can get more range out of the volume control. No loss of treble at all and no change in the bass-treble balance. Good in every position, though the neck & middle position is the real star.