I travelled by myself, without permission slips from my parents or anyone else, to 20+ countries before I turned 18 (primarily while 16 and 17). Airlines don't care. Train operators and bus lines definitely don't care (with very few exceptions, nobody will even ask you for ID for these).
Hotels are the only place that you may run into problems; officially, many places have a rule excluding guests under 18 (or, in the US, 21). In reality, in my experience, this is never enforced if you look responsible and have a shiny credit card. Unless you give them reason to, most hotel clerks are unlikely to even bother looking at your ID long enough to notice your birth date. With lower-end properties or hostels, you are even less likely to run into any issues.
Overzealous immigration officials could be an annoyance, but assuming you can clearly articulate what you're doing and where you're staying in their country and show that you have funds to support yourself, it is extremely unlikely that you'd find yourself deported back home. In my experience, the only countries that ever even commented on my travelling alone as a minor were the US, Canada, and the UK.