Cape Town to Nairobi on a Vespa PX200EFL, 10" wheels, and 12 HP. Then again on the 9000 km Budapest to Bamako Enduro Rally (also offroad bits like the moroccan deserts, the beaches of Mauritania, pistes under construction, etc).

I've also done a fair bit of travel on a Yamaha 50 CC DTR.

I still don't consider any of those adventure bikes - they are capable, but unsuitable - and they don't fit with the most agreed upon form factor concept (factory ready bikes advertised as adventure bikes). My Yamaha WR250, or the Honda CBR 600 F - same thing. Their intended use is completely different - though no doubt thay adventurously could take me just about anywhere if I was so perversely inclined. My old BMW F600GS Dakar on the other hand, fits well within the most agreed upon concept as of what a factory ready adventure bike is... as would the Yamaha XT 660 Z Tenere that I currently have my eyes on.

Although interesting to have a discussion about trying to define the term - I find that when questions such as "what is the best adventure bike", quickly turns into a rethorical debate rather than simply trying to answer the question within the most agreed upon definition of the term - the one the poster probably thinks of (otherwise the poster would most likely have supplied; a broader definition of the term, a different definition alltogether, or ask for the definition to be challenged???

So to answer the question of the poster - as most modern factory ready adventure bikes seem to start at 50 HP (one cylindered thumpers) - with few severe complaints as far as I can see, I would say 50HP for one person is more than enough. And as for those riding two up and hauling a ton of stuff - usually finding a larger bike more accomodating for two up - usually having bike choice reduced to options with more than one cyclinder and more than 70HP. I believe approx 85-110 HP is more common choice than 70, with for instance the F800GS starting at 85 and the R1250GS delivering a whopping 136. I've never heard any complaints of having too much power, and I have not heard any serious complaints of from someone only having 85 HP either. I frequently hear complaints of the bike being too heavy or big.

Now, sinking thousands into kitting for instance a WR250R (30HP) could make a great adventure bike (enough power to get you over tall mountains, ride off road, do ok on the highways - and keeping the weight low). But - it isn't a factory ready adventure bike.

So, 30 HP for one person, and 70 for rider plus pilion - seems more than enough - though most selections would probably start at 50/85 HP for 1 or two people. You could still probably cut that in half and still have enough - but why would you if you didn't make any significant gains in other places? No point in actually trying to find a weak bike?

The 70 vs 85 HP does make a significant difference when riding two up, especially on faster roads where you need to pass other vehicles, etc. But I don't need a bike so powerful that the pilion will fall off if a twist the throttle all the way.

So, for me, the lower limit would be 30 hp for a kitted dual sport (one person), 50 hp for a factory ready adventure bike (one person), and 85 for a factory ready bike for two people (seing few arguments of trying to kit a non factory ready adventure bike for two people).

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