I made the trip to Alaska and back as a kid with my dad and grandpa in 85. Back then we took a spare everything and two full tires and wheels, used both plus a repair. Fixed radiators twice and a leaf spring.
In 2016, the trip is much easier. But...it is still long, parts of the road do shake things loose, and on top of all that...the regular old stuff happens. So...bring one of everything and maybe a couple of some things.
Bryan packed a full set of tires. I carried a full trailer spare already assembled. We both have tubes, he has bearings, three of us have full tool sets, I have electronic manuals for everything on a kindle reader, etc. We have way more than this stashed on the bikes and in the trailersame like tire repair, electrical stuff...
Also...I recommend a travel buddy on a trip like this for so many reasons. Remote travel, moral support, help, extra eyes. Reamer 2 noticed the trailer wheel flopping before it departed for destinations unknown...only a travel buddy would have noticed.
Last...consider trip insurance. Medjet, maybe goodsams, maybe regular trip insurance. We all know why we need insurance so don't overlook it in your planning.
There...my only preachy post of 2016. Probably.