Pros: Traveling on your own gives you total freedom: you can do exactly what you want to do, see exactly what you want to see, eat exactly what you want to eat, sleep exactly when you want to sleep, and so on and so on. You're sure to meet amazing new people on your journey, but learning to be content with your own company is a powerful lesson in itself.
Cons: Being alone can be, well, lonely, and some experiences feel hollow when they're not being shared. Also taking pictures with the self-timer on your camera is a pain in the ass.
Take the trip if... you need to do some solo soul-searching, or even if you've just never traveled alone before: everyone should take a trip on their own at least once in their lives.