I bring a DSLR camera with a normal zoom as well as a separate telephoto zoom and a small tripod.  I enjoy photography and travel with the telephoto mounted in the early hours for wildlife.  I take "selfies" at state lines and such by mounting the small tripod to the seat of my bike - the bike is held up by a click-stand.  So then, "real" camera gear is a must for my personal enjoyment - and the click-stand and parking brake stretch-bands that enable me to park my mount upright anywhere. 

I bring a netbook (lightweight) computer to do journaling, instead of getting by with just a phone.  The camera gear and the computer add a few pounds of weight to my load, but I consider them to be necessary equipment for my tours.  Yes, I COULD make do without them, but without the DSLR and telephoto lens, how am I going to capture that perfect wildlife shot?  What if I see Bigfoot out and about in the early morning? 

On my 2 longer tours (4,000+ miles) I have carried camping gear and my jetboil stove.  I almost consider the jetboil to be essential gear, because it sure is nice if you have found shelter somewhere during a cold rain and you can warm up with a hot cup of coffee or cocoa.  On my shorter tours (< 1,600 miles) to date when I have planned to always stay indoors, I have not taken the jetboil - but inevitably there will be at least 1 day when I wish I had. 

Riding on Panaracer Tourgard Plus tires, I have not needed steel tire irons - the hard plastic versions work fine for my needs.  In fact, if I use very good technique, I can  mount the tires without any mechanical assistance, but it's quite helpful to have the plastic "irons" when removing the tire. 

My touring bike is the first one I ever had that was built with a dynohub.  I now consider that a "must," the convenience of having lights 24/7 and never worrying about charging them is wonderful.  I never even turn the lights on or off - I just roll away and voila!   So that's a must for me, and any future new bike will get built with a dynohub. 

And lastly, just because it's my defining thing as it were and I've been "recognized" by others I never met because they knew of it, the Hula Girl who rides atop my rear rack is an absolute must for me.  No one can accuse me of being a weight weenier, I prioritize utility and even "pizazz" over a few pounds of weight reduction.  

I bring along some 'pizazz' as well. When my son was a wee lad he'd carry around a tiny little white bear named Pookie. Pookie has been pizazzing all of my trips since 2006.

A chair is a must for me....

Our must do /  haves:

Over the years everyone has developed a neat trick or two - here are a couple of ours:

1) on booking.com comments - after you have made a booking  - we always say that we will be arriving by bike and will need storage. If there is going to be an issue, best to get that out of the way early. When you do arrive the hotel they are always ready for you.

2) we travel with Bike Fridays and take with us two thin rolled up nylon bags. These bags have saved us many times. There is not a train, bus or hotel room rule that has restricted our movement.  We even have used them on unplanned aircraft bookings.

3) A ball of twine for a clothes line to dry our clothes should they get wet our when we wash them.

4) A small collapsible dolly that we use to transport our  panniers that we carry on the aircraft. We leave this behind with our suitcases. It makes moving about the airport so much easier.

Great question.

On bike boxes I always write, "TSA OPEN THE END" and draw an arrow pointing to the end for TSA to open. TSA agents have said they appreciate it. 

When bike camping, I bring a UCO tea candle lantern. It gives me a sense of emotional warmth and has a centering effect at the campsite. I almost never start a campfire even when fire rings and wood are available. I'd rather be noticed for sweat and road grim than smoke and ashes when meeting civilization.

For electronics I find a multi outlet AC charger, a multi outlet battery pack and a broad assortment of USB adaptors are nowadays a must. I was treated to diner and beers in Spain after supplying the necessary gizmos to charge a fellow biker's phone.

I always carry a Fiberfix spoke. It's a clever kevlar cord that is used to replace a broken spoke. 

Another must is a folding spare tire. I once had a tire's sidewall blow out and didn't have a spare tire. Not fun.

Me too, if I'm camping.  If not camping, I don't bother with the chair.  Yet.

Years ago I had a multistrand elastic clothesline that I bought in a travel shop.  It finally lost its rebound and so I made a new one with thin shock cord (which I braided) and a couple of cheap carabiners.  No pegs needed, just stick the sock or whatever between the shock cords.

Thanks for starting this thread, Brent.

I'd say, "Most of the above," even if not all of the specifics are on my list.

Like you, I use a nice digital camera on tour.  In my case, it's a lovely wee Panasonic Lumix ZS40, which I've had for a decade now.

I have my own take on plastic wrap for the bike box:  I carry a roll of hockey tape, made in Renfrew up the valley.  Lugging my bike box around European train stations in 2012, baffled by the absence of trolleys, I said "Sod it,", and taped the lower corners on both ends.  Voilà!  Effective lightweight skid plates and no more lugging, just dragging with one hand.

There are a few items which I find invaluable but which haven't been mentioned above.  A few zipties are hugely useful for all sorts of odd mechanical misfortunes.

Then, there are these, which I find essential for Life In General, hence for touring:

The Swiss Army Knife is a well-known device, obviously.  This one was made by the Wenger factory (no relation to Arsenal's manager, AFAIK), after that firm was taken over by Victorinox.  Accept no substitutes.

The other two items are 4" and 8" Quick-Release rubber ties. I bought these from Lee Valley Tools, in quantities of 25 of each. The little ones cost about 25¢ each, the big 'uns about 50¢.   (But, despite my entreaties, LVT inexplicably no long sells them, so now they are available only from agricultural/vinicultural suppliers and in vast quantities -- they're used for fastening vines to poles and wires.)

I use these for all manner of things in Life In General, e.g.:  The 4" ones, wrapped around a pair of D-handles on kitchen cabinet doors, protect the cabinet contents from our granddaughter's curiosity and vice-versa.  Ditto our precious hoard of vinyl LPs in the lower cabinet of our audio system.  The 8" ones  effectively and cheaply eliminate wheel flop when wrapped around the front wheel and downtube of a stationary touring bike with loaded front rack-and-panniers.  The 4" ones are ideal for holding open a vestibule door with a tent peg -- the flex in the QR tie absorbs the tug of a stiff wind.  The 8" items, singly or doubled, are ideal for compressing bulky clothing into manageable lumps. Etc., etc.

Cheers,  John