At least a simple mixer is essential to provide gain & tone adjustment of microphones; what is required is dependent on application. From the very start we were expecting to be working with bands, so we needed a relatively complex mixer.
We use a twenty input Spirit Folio SX mixer; twelve mic inputs and four stereo line inputs (two of the latter are used for reverb and music sources). Very usefully it has three auxes with individual output level controls, useful for monitor mixes (two separate ones if the facilities are available) as well as the reverb/effects loop.
If twelve stage sources isn't enough, I add a small battery mixer for an extra five channels. I also intend to add a very basic mic/line mixer of eight XLR inputs mixed together with variable gain; both the latter mixers would obviously be useful as standby mixers - I like to be prepared for equipment failure if in a field in the middle of nowhere for the weekend.
Mixer power supplies are often a pain, most require a double rail supply of more than 12v - this desk requires a power supply of +/-18v. This is derived from the internal power supply of the power amp (+/- 46v) - each rail is very simply dropped down by a large resistor, to avoid the mixer internal regulators being overloaded. The alternative would have been to build or buy a custom +/-18 (or 15v) 12v power supply, at around fifty pounds.
Eight channels is barely enough for bands; I've had to combine microphones into one channel before, and am working on getting a mixer with more channels to use on the system. For simple acoustic acts, or just speeches, four, or even two channels can suffice.
A very few commercial mixers will run from a 12v supply, mainly designed for portable broadcast use, and unlikely to be cost effective to buy. It is also possible to design & build mixer circuits that will run on a single 12v rail; as mixers get bigger the time and effort required to get a useful and reliable result makes it less worth while to build your own. It's useful to be independent of other kit, though, so the very simple emergency mixer I mention will run from the standard 12v supply, whilst the proprietry battery mixer runs from two PP3 batteries.
(add Compact 4/10 mixer, DIY links)