Minimum mountain bike trekking/touring equipment
The answer to your question depends heavily on the infrastructure that is available to you, and the highest level of mechanical ability in your party.

As another pointed out, you will want at least two pumps, multi-tools, etc.
  My wife and I do pretty challenging mtb tours with BOB trailers. We generally bring the following (subject to modification depending on how present bike shops might be). 


for disk brakes, at least one set of extra brake pads for each type used (e.g. my wife as avid, I have deore xt, so we bring one pair each).  When riding with extra weight, it's shocking how fast brakes can wear away.
two spare spokes for each size used.  These can be taped to your bicycle frames, so they won't affect your packing at all.  Breaking a spoke can end a trip if you don't have a spare.  At least learn the theory of how to do a field repair.  It doesn't have to be perfectly true, but you want to be able to at least roll into a repair.
at least one spare tube of each size in use (you want patches too, but you may need the spare for a big cut).
duct tape. You'd be amazed how this can help you. I've fixed panniers, packs, rain-gear, sleeping bags, and patched a ripped tire.  This can save a trip.  Make a small roll for yourself, you don't have to take a gigantic one.
Consider your water needs.  Water purification can be a life saver.  My wife and I use a steri-pen, which we love.  What you need depends on where you are going. When we rode across Albania, my wife and I brought a ten litre sack of water with us, which may very well have saved our lives on a couple of occasions.  In the alps we just brought 2 litre camel-backs and filled them up at the many opportunities.
bike lights are a good tip and will be useful at camp time.
Unless you are sleeping indoors, you must bring bed rolls.  Depending on the weather you might be able to do without a sleeping bag, but an insulating layer between you and the ground is vital.  I can't stress this enough.  Therma-rest makes small, light and highly packable bedrolls.  Cheap foam rolls are an alternative, and are light but  bulky.  On the plus side however they are virtually indestructible.  You can roll them up and strap them to the outside of your backpack.  At a bare minimum bring enough for your core (neck to thighs).  You'll sleep for crap if you don't bring something to put between you and the ground.  
A first aid kit.  REI sells nice, small, packable, reasonably well fitted kits for a reasonable price.  At the very least, bring some bandaids (for blisters), some sunscreen, some painkillers, and some antiseptic.
I highly recommend bringing some kind of emergency contact gear.  If you are somewhere with cell reception, a cell phone is enough.  If not you should consider bringing flares or some such.
Saddle cream.  Unless you are routinely doing that kind of mileage now, you'll be really happy to have this.