On my longest tour, the (old type) headset top nut loosened up a little bit. Notably, that was the ONLY issue.

Normally, I would say tire punctures/disintegration is the most frequent issue.
I try to start out with new or freshly serviced components and drive train, so I don't have as many surprises.
I think my first (or nearly first) tour involved some derailleur spaghetti.

I am at the age now where I am far more worried about the components on my body breaking than on my bike. I can pretty much fix anything on my bikes, given the tools and parts.