Ooh, I just saw this thread for the first time. I've backpacked a lot in Europe and New Zealand/Australia so I have some things to add that may be of interest. There's some great advice here already though!
Throughout my backpacking/roaming I've mostly stayed in hostels, with couchsurfing visits here and there. I don't know about Japan but I would agree that hostels in Europe are generally safe, and that HI hostels have a good standard of accommodation if you want to be sure the place you stay isn't disgusting. Based on my experience they seem a little quieter and less "party" oriented, which may suit some and not others. I wouldn't discount independent hostels, there are some really nice ones out there and truthfully, most of what will make/break your experience staying in a hostel is how nice or annoying the other people staying there are, which is totally unpredictable. Oh yeah, and some hostels have private rooms with shared bathroom facilities, but they're a lot more expensive than the shared rooms and tend to book up quickly. If you're visiting anyplace during their high season I would suggest booking at least a couple days in advance. I used to use Hostelworld.com sometimes, because there are lots of user reviews on there (so you can get kind of a feel for a place if you're apprehensive) and also you can book online. Generally speaking hostels are very social places, which can be very good when you're travelling alone. I still keep in touch with some people I met whilst backpacking in New Zealand! If you plan on staying in hostels during your adventure, I would plan on packing a lightweight padlock and a lightweight fast-drying towel, as hostels will not always provide those things and they're useful to have. As others have mentioned, one of the other benefits of hostelling is that most of them have kitchen facilities so you can cook your own food!
OK, now for some potentially confusing stuff about travelling long-term in Europe on an American passport: Regarding planning, I would try not to get too bogged down planning everything in advance, though if you're travelling to most places in the EU with a US passport and no return/outgoing flight from the EU booked upon arrival, the people at immigration might give you a hard time. They will ask you a lot of questions about your travel plans, and may also ask for proof of funds sufficient to pay for your trip/a return ticket (bank statements would suffice in this case). This is obviously to weed out people who are trying to enter the country to live illegally, which you are not planning on doing, so it's good to be prepared with documentation in case they do ask for it. You can of course avoid that if you book a return flight to the US from your point of entry/another major European city, or an ongoing flight to outside of the EU into a country you are legally allowed to enter (like if you booked a flight from London to New Zealand, since Americans can visit NZ without a visa, though you might have to do the same song and dance when you arrive there). You should also be aware of how long you are legally allowed to stay in the places you plan on visiting without a special visa, so you don't overstay. The last time I checked it was 6 months in the UK, 90 days in the Schengen area for Americans.
Lastly, if you are under 30 years old have you considered the possibility of doing a working holiday? Basically what that means is you get a special, temporary work visa that lasts for a year (or longer in some cases) so you can travel a country extensively and also do temporary work while you're there to help fund your stay. As far as I know US citizens can't really get a working holiday visa anywhere in Europe, but if the idea of exploring/working in New Zealand or Australia interests you then that might be an interesting adventure. Australian working holidayNew Zealand working holiday