The microphones I use would make a long list. There are specific microphones that work best for a pattern of circumstances. Thus, there are microphones that work best for drums, vocals, choral, stringed instruments, electric gtr, piano, and so forth.
Since this is a hip-hop forum, I believe the focus of microphone usage is mostly on voice capture for a song. Thus, the utilisation of microphones must cater not only to the broad general terminology of "voice," but different microphones work well with male and female voices. Furthermore, the type of dynamics a rapper or singer has in their delivery also necessitates the need for what microphone may properly be used. An extreme example are the Rolling Stones. Mick Jagger's vocals lacked the desired intensity when he was placed in a booth in front of a condenser microphone. The producer thought it best to have him roam free in the studio singing (and holding the microphone! imagine that!) through a dynamic microphone instead, since Jagger could move around and put more emotion into the performance.
All these weigh greatly in utilising a microphone.
Yes, I use Neumann, Schoeps, AKG, Sony, RCA, EV, and different vintage microphones for different projects. It depends if you're recording a voice, etc.
As for mic amps, I usually run off the board. It depends what board and what studio I'm in. Some old but good Neve 1080s were recent mic amps I used.
Sincerely,
God