All of these mics need power to operate. I think Guysonic's and Church-Audio's mics can run off the plug in power of small recorders. They'll correct me if I'm wrong I'm sure. Still, most of these will perform better with a dedicated battery box or preamp that provides a bit more voltage, especially at higher SPL levels. The DPAs will not run off lower voltage plug-in power from a recorder and require a battery box or preamp (a possible exception is the low voltage 4063 version that Jeff uses for that very reason, but they are not very common around here). If you are recording anything where the self-noise of the mic could be even close to being an issue you'll probably want a preamp since the higher gain settings on handheld recorders typically get noisy.
The 4060s can use the DPA preamp designed for them (MMA6000) or many other smaller preamps such as those sold by Guysonic, Church-Audio, Niant, Sound Professionals, Core-Sound and others. There is the DPA micro-dot connector to deal with, either by re-terminating the mic to something more common, by building the preamp with micro-dots, or by making an adaptor cable. You can also power them with a recorder or preamp that provides phantom power by using DPA XLR to microdot powering adapters (or building your own, circuit diagram is avaiable).
I use Church-Audio CA-UGLY preamps with my 4060s because they are the smallest avaiable and seem perform comparably to the MMA6000 to my ears.