Do we get to bring an assistant to carry stuff as well?
For me, I'd bring an OM2n, with 24mm f/2.8, 35mm f/2 and 85mm f/2 lenses - all Zuiko, of course.
And an OM1 body as a backup.
All of which will fit in a small bag - I could even add a T32 flash!
Ok, I'll play.
Olympus OM-1n with 1-10 screen
24mm f2.8 Zuiko
35mm f2.8 Zuiko
85mm f2 Zuiko
Big bag of film.
I'll take a Nikon EM and 28-50-100 or 135mm lenses. That's normally what I take.
Why? Mechanics can fail too...
In revisiting this thread, I've noticed the answers above, including my own.
These days I'll agree with baachitraka. A mechanical camera can fail.
For a year around the world with just one camera, it is a bit unrealistic not to take another camera in case the first one develops a problem.
There are many stories of cameras failing when you most need them. It can happen even with the most rugged camera, be it a Nikon F, a Nikkormat or any Leica.
For myself, I will always remember the time I was using a Canon EOS-1N on the Golden Jubilee weekend: one morning, loading the -1N with fresh film on the Mall, the PB-E1 motor drive failed and won't advance the film. Fortunately I had a EOS-3 with me and it was Saturday. As the PB-E1 was new to me and under warranty, it got swapped for another one.
I was saved by having a backup with me.
I would swap the EM for a FG or a FE or take both the EM and the FG.
Although I am using an OM outfit as well as now, I have concerns about the mechanical reliability of the -1 and -2. They can develop a problem with frame spacing and the interlock. I have seen samples of both problems.
One word of caution: if you can't press the shutter button, never force it as a small piece can brake and the only solution is to find a donor body with that piece still intact.
Still for a OM setup, I would take:
OM-1N and/or -2N
28mm /2.8
35mm /2.8
50mm /1.8
That is what I use 95% of the time, particularly the 35mm.
I've noticed that both the answers above refer a 24mm and the 85mm.
Myself, I find the 24mm a bit too wide and a 85mm not to be as tight as I would like.
For a dream OM outfit, here it goes:
OM-3TI
28mm /2
35mm /2
50mm /1.2 or 100mm /2
That would do nicely.