How do I get the pads out of my Avid BB7 disc brakes?
I've been pulling them out a lot lately. They do come out easily, but only if you have the adjusters all the way withdrawn on both sides. The catch is that the adjusters (at least the ones I'm working with) can start seeming tight before they are backed out all of the way. So backing them off can be a bit of a judgment call.

Update: I was doing the "holiday overhaul" on my partner's bike and I was also sorting out why the brakes were hanging up a bit (corroded cable) and noticed another thing that can make the pads harder to get out than they ought to be – the actuator arm wasn't releasing all the way because the cable was a bit too tight, so I was missing maybe 5 or 6 mm of travel when the brakes were released.

Once you've got them all the way backed off and the wheel removed, pinching the tabs together and centering the pads in the caliper opening should let them come out fairly easily. Sometimes, I find that it helps to hold the pads all the way to one side and slide the one towards the center out a bit and then reverse the process. There is a pin in the adjuster that secures that pads and if you don't clear that they will hang up. Often when the pin hangs up you naturally pull out the other pad a bit. Once one pad is past the pin, pushing it towards the side and pulling the other one should be enough to get the whole assembly out. They come out with very little force.

There is nothing that will stop you from pulling the pads out one at a time, just move one towards the center and pull it out, then do the same with the other one. If you do this, you're likely to leave the spring behind, but it is relatively easy to coax out with a pair of tweezers or a pointy object or even a blast of air from behind.