Some of the best trips I have ever taken in my years of travel have been on a motorcycle that I either rented or bought in a particular country and then just hit the open road, many times without a particular destination in mind. My favorite one of these memories was where I had 2 other friends with me that share that sense of adventure and we just headed in a particular direction on a winding minor highway and didn't even know where we were going to stay for the night.
It doesn't have to be a particularly good motorcycle, but it would be helpful if it is somewhat reliable or if you don't have that aspect, then a knowledge of basic repair is probably a good idea, which thankfully I have.
Fortunately, in most countries where motorbikes / cycles are a popular method of getting around with the locals, you are never very far away from a motorcycle repair shop as people seem to set them up in their garages every kilometer or so and if you break down you can have your buddy push you.
I have been in multiple situations where someone did this for me and there does seem to be a real skill for it - one that I do not possess. If you are traveling with some friends it is probably just a better idea to have them run ahead to a motorbike shop and get the shopkeeper to come and help on the spot. Sure, language barriers are going to exist but I have never been in a situation where some good ol' pantomime couldn't sort the situation out.
The reason why this form of travel is so much better than any other is that you have the ultimate freedom: Buses and even worse tour groups are only going to go to major sites and sometimes the best and most unique things are off the beaten path. I have seen amazing waterfalls that were too far away from major tourist areas to be a viable destination for these tour groups and have also ended up spending the night at amazing "resorts" that foreigners likely don't even know exist. We just happened upon all of these places as they don't even appear on maps.
We would just see a blue sign telling us that a waterfall was "thataway" and we went for it. There are some great finds in these places and since there are no foreign tourists at these things, most of the time the usual annoyances of tourist traps and dual pricing systems don't exist there.
This amazing waterfall located outside of Trang, Thailand had almost no one at it and there was entrance fee or even anyone harassing you to buy snacks or souvenirs. This is not visited by any tour group that I am aware of and we basically had the place to ourselves.
There are many dangers associated with motorcycle travel of course and for that reason I would never recommend it to someone that doesn't already know what they are doing. Road safety is all but non-existent in many countries around the world so anyone expecting some sort of order the likes of which would be found in North America or Australia needs to realize that while there are road laws in developing nations, nobody really adheres to them. The best thing to do is to treat yourself as if you are invisible because the motorists are going to treat you like you aren't even there. This has nothing to do with the singling you out, it's just the way that it is.
Also, even if the country you are in is very hot, you should still wear safety gear including long pants and sleeves. Even a minor slip can result in major road rash if you choose to not do this. I learned this one day when wearing flip flops like a dumb shit and lost a ton of skin on a foot just from touching the road in a turn.
Also, you gotta remember to put sunscreen on any exposed body part including your hands. I ended up with rather extreme sunburn on my hands after a 4 hour ride and looking back, that was incredibly stupid on my part because of course your hands are going to be exposed the entire time!
There are many dangers in this form of travel, but just like most things in life there is a tradeoff between risk and reward. As long as you take it easy and always keep your head on a swivel, you'll be fine and you'll also experience things that most other people never get a chance of seeing.