My job involves helping my boss film academic talks and presentations.
This involves ensuring that our cameras and wireless mics and whatnot do not die.
Our rationale is that the potential cost of having batteries of an unknown age run out during a recording is greater than the cost of just replacing them every time we shoot.
I personally tend to use the mountains of half-used batteries to power my remote controls, alarm clocks, and RC helicopters afterwards.
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For anything that can be powered directly (stomp boxes), do that.
There are power strips that will lock down your transformer bricks, and also breakout boxes that will provide you directly with a number of DC terminals.
Wireless mic battery packs should be replaced for each performance.
Unless you're only performing for a small group of people and the space is intimate enough to offset needing to take time to change a battery pack, you're going to want to avoid that kind of disruption at all costs.
And yes, this means that in, say, a musical production with 15 wireless mics and four performances (plus two dress rehearsals), I'd budget for 60 batteries (Duracell) plus 30 for dress rehearsals (store brand for these).
What you do with them afterwards is up to you, just don't chuck them in the trash--find out how to recycle or dispose of them properly if you can't give them away to be used.
music.stackexchange.com/users/133/NReilingh
When I was performing I used a power adapter for my stomp boxes.
There are splitter cables for connecting the stomp boxes out there.
For example: http://www.guitarcenter.com/Dunlop-DC-Brick-Multi-Power-Supply-105495402-i1124423.gc#
music.stackexchange.com/users/924/DimebagFan 
For floor hardware, use transformers wherever possible.
Just use batteries in mobile kit, and always use brand new batteries for a live gig.
Those ones you take out can be used in rehearsals or the studio until they die.
Keep a battery case in your gig bag - for 9v batteries
you don't want them discharging against each other or against sensitive kit
so a case will hold them safely and insulated from anything else.
New batteries stay in their packaging until use.
Used batteries stay in the battery case until discharged, then delivered to recycling.
music.stackexchange.com/users/104/Doktor Mayhem
As others have said, use transformers wherever possible.
When batteries are unavoidable, use rechargables and recharge them fully for each show.
With one recharge cycle per week, common NiMH batteries last about 3 years before their capacity degrades so much they won't last for 2 hours (down from ~4 hours in the same application).
Recently I've started using NiZn batteries for our wireless mic transmitters.
These are brilliant: more than 8 hours on a charge.
They produce 1.6 V rather than the 1.2 V of NiMH cells
so you don't get problems with devices that want more than 1.2 V.
music.stackexchange.com/users/45457/Hobbes
Many musicians use battery-powered "stomp boxes" and wireless microphones.  When do you change the batteries?  You can't have a device running out of power halfway through the show.  Do people put in fresh batteries for each show and give away the half-used ones?
Managing batteries for live performances
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music.stackexchange.com/users/113/Mark Lutton
For performances, you should use direct power as much as possible. Mic batteries should be replaced after every performance. It's generally agreed that the best routine is to replace batteries with fresh ones before every show.
It's generally agreed that the best routine is to replace batteries with fresh ones before every show.