Typical world travelers plan to see world by their own motorcycle, I meet such people often. They ship their bike place to place, store it for around a year or something and see places around. Would’ve been lot of logistics for me so decided to rent one. Riding a motorcycle in many parts of the world is challenging and scary as hell.
Safety concerns
Riding is always not safe, specially when you are riding an unknown motorcycle on unfamiliar roads/conditions. You choose your own level of acceptable risk. Many people set off on road with motorcycles out of their experience levels, sure more power is always tempting but there has to be a fine balance.
Rental options
Most of my experience has been in Europe and South East Asia, it is very difficult to rent anything bigger than 125 cc at these places. Scooters are common in Europe. There are options to rent larger bikes, you may have to search on local forums or ask hotels/guides. Sometimes individuals may agree to rent you one, just check if its legal in the particular country to rent a non-permit vehicle.
Whether to get a Enduro, Dual sport, sport is entirely on you. Depends on where you plan to go, your size, experience, preferences, what you plan to carry etc.
Paperwork
Many countries may want an International driver’s permit in addition to native country’s permit and passport, just call the rental agency and ask before hand. Its fairly easy to get IDP here in USA. Medical Insurance, motorcycle insurance are a must, you don’t want to end up paying for heavy damages/liabilities in case of an incident. Many rental locations will provide you an option to buy insurance from them in case your own insurance is invalid outside home country. Credit card for security deposits.
Quick Checklist
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Driver’s license -
Passport
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International driving permit
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Rental vehicle registration papers
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Credit Cards
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Helmet (rental location can also provide one)
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Protective gear (I prefer to carry my own instead of renting)
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Emergency toolkit
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Handy maps
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Emergency phone numbers
My rental experience with IMTBike in Portugal
IMTBike is a motorcycle rental and a tour organizer operating mostly in Iberian region (Spain and Portugal). I’ve learned that they officially partner with BMW Motorrad, hence your rental options are limited to Beamers, nevertheless, amazing machines.
I was in Lisbon, Portugal that I decided to rent a bike and go cross country. The rental experience was so friendly, the location manager kept the store open afterhours for me and helped me with everything. He gave me a tour of his facility and spoke about things on what to do and what not. His experience riding in Europe really came in handy. Even lent me his personal rain suit in case, he just let me have it. Bike was really well maintained and clean. I picked up a BMW F700 GS, not one of those huge tourers since I am a supersport person so a tourer would have been a lot.
Of course I missed the grunt and power in this adventure bike but was so smooth. He gave me a good briefing of the routes and rules, helped me find a safe parking place near hotel. That small meeting ended up in a friendship. I did about 800 kilometres (Lisbon-Coimbra-Porto-Sintra), absolutely no issues with the bike. I won’t say renting from them is cheap but definitely not expensive for what you are getting. Highly recommended 
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