Let's take a look at how the Hammond B3 is best captured. Remember, these mic techniques can be used for both studio and live sound applications.
Microphone SelectionDue to the unique sound of the Hammond B3, microphone selection is very important. On the Leslie tone cabinet, you've got two distinct rotor sections - the high tone and low tone. The rotors work together to produce the overall sound of the B3.
For the high tone, you should consider micing in stereo if you have the resources to do so. Good microphones for this includes the Sennheiser MD42, the good ol' SM57, or any other good small-diaphragm cardioid microphone.
You may also wish for a more permanent installation for live sound or recording in a studio; the Shure Beta 91 is a great choice -- they lay completely flat, and can be mounted in stereo without getting in the way of the high rotor.
For the low tone rotor, you'll want a microphone that can really handle low-frequencies best. Your ideal options are something similar to the Sennheiser E602 or Shure Beta 52 In a pinch, a Shure SM57 will work, but it's preferred you try one of the other mics if possible -- you might like the response of a more bass-sensitive microphone. Again, a single Shure Beta 91 will work, if you prefer - you're not needing to record the low rotor in stereo for doubling like you do the high rotors.
Microphone PlacementThe low rotor is the easiest to mic, so let's go there first. Just simply place the microphone near the rotor outlet, and give yourself about 4 inches of space from the rotor itself. Depending on the microphone used, you may need to move it closer, or back it off. Make sure to pan this microphone center. The high rotor is a little trickier.
You can do two different techniques here, depending on your needs and resources. For most live sound situations, a single mic will do fine, and if you're in a crunch recording with track space, you can also use a single mic, pointed between 4-6 inches away from the rotor opening. To use a second mic, place it 180 degrees away from the other microphone on the opposite side. Pan these channels right/left based on your needs. You'll find that bringing up the high rotor mics first, then filling in the low microphone behind it will yield the most balanced sound quality.
Mixing To PerfectionMixing the Hammond B3 is actually very easy. You're going to be combining the signal you're receiving from the top two microphones and the bottom to create a stereo image of the instrument.
In your mix, you'll want to pan the high microphones left and right; you'll need to make sure you paid attention to the phase of the two mics, but if you did things properly, you should get a wide stereo image. The low rotor microphone will remain centered in mono, along with the bass and core drum tracks.
Using this simple technique, you'll get a huge, live-sounding B3 track; this fits expertly as long as the aesthetic of the song demands it.