I'm an Electrical engineer... And I have been looking at options. Right now I'm traveling RTW but I a couple years I might try out electric options.
Current bikes have a max rang of about 150 miles. So if you did this in a day, it wouldn't be limiting. Quick charging usually takes 2 hours, but regular charging is overnight. Unless you added more batteries, the range might be a problem in some countries. I would think traveling around Europe on an E bike would be great though. I think offroad will be a limitation for any electric bike. Sure there are offroad electric bikes, but the range goes way way down.
I've been keeping an eye on the Brammo Empulse Brammo 2014 Empulse & Empulse R
I like this one because it still has a 6 speed transmission. I like the idea of shifting. I think a single speed electric bike would limit fun.
Zero Motorcycles also makes some decent bikes. A friend of mine has the Zero FX and he loves it. He puts it on the back of his overland rig and charges it while he drives from camping spot to camping spot. 2014 Electric Motorcycle Model Line || ZERO MOTORCYCLES
2013 was the first time an electric motorcycle won overall at the pikes peak hill climb. The Lightning electric motorcycle beat every single gas powered bike. When you think about it, it makes sense. Amazing torque at all ranges and you don't loose ANY power with elevation. Its a sprint not an endurance race so that also benefits the electric bike.
Lightning's Electric Superbike takes 2013 Pikes Peak International Hill Climb
Charging with solar panels is feasible for someone who is using the bike as a commuter. The solar array would be to big to carry with you though. Maybe if you went very small like an electric bicycle, but then you are charging during day and riding when? 1 day ride, 1 day charge? Ride in morning and evening, charge in middle of day?
I like the idea of plugging it in at a hotel, hostel, or house where you sleep. Give them a 2 or 3 $ for the power and continue in the morning. If I was doing it, I would even have a meter to show them how much power I took so I could compensate accordingly.