It depends on what parts I am looking for.  Some I am able to get from vendors, while for others I go to Brownells.  I try to keep enough on hand in personal stock that I can teach a class and fix a weapon on a lunch break.

Below is what I bring with me.

Thanks.  I started with this a few years back to keep small parts together, but it turned into something that I bring to courses.  The military side of me wants to tell people "YSIW!" if their weapon breaks in a course, but the soft side of me figured swearing at a guy who borrowed a friends weapon to take a course wasn't helping anyone.

Things like a disconector springs, hammer springs, gas rings, or extractors I usually just replace out of my own pocket and never charge the owner.  Most of these guys/ gals are fellow officers, and I tell them to just buy me coffee down the road.  

I've kicked around the idea for awhile of premade AR15 spare part kits, but I think everyone really has their own version of what needs to be done.  A basic kit in my book would be a full LPK (CMT) along with a CMT MPI bolt organized in a small tackle box.  Other people would probably think basic springs and extractor setup would be a great basic kit.  Either would probably be good depending on what you do, and how many people and weapons you are trying to keep up and running.