It is expensive coming to Japan to do the teaching English, living abroad experience. What you may not know is that it can be quite expensive to get home too!
If you came on a return ticket then you are set. If you came on a one-way (or let your return expire), then you will have to find a flight home. This shouldn't be a surprise, but it is worth setting aside money from the start for this, so that you never get stuck needing to put it on your credit card. (Don't let your parents pay for your ticket because these day you have to show the credit card you paid for the ticket with at check-in!)
After you have completed a contract, you may be left with a bit of time to spend sightseeing. This always takes a bit of cash, even when doing it on the cheap. Just make sure you are aware of the surprise costs below, to ensure you don't find yourself short of cash at the beginning of the last month in Japan you set aside to "bum around".
Your income tax bill in Japan is based on your income earned in the previous year. So if you go home after your first year, you will be safe from this (you may have a small bill, it depends on when you come and when you leave).
If you stay for the second year or longer, then you will be paying a normal income tax bill, but unlike when you are staying and can pay it off in quarters, you will have to pay this bill all in one go. For an average ALT/JET salary of ￥200,000 - ￥300,000 per month, this will equate to a bill of about ￥150,000 - ￥250,000.
Note: Income tax rates differ based on where you live.
Cleaning has become mandatory when you leave an apartment. Regardless of how well you clean your apartment, more than likely a cleaning company will still be hired to clean the apartment after you vacate it. This fee will be in the range of ￥30,000 - ￥50,000.
If you aren't close to Tokyo, then getting there can be costly if you use the shinkansen. You can save money here by taking buses (or a night-bus).
If you are like most, you will have accumulated a bunch of stuff over the year or so that you were here. Some stuff will just be rubbish, some you will give away or sell but there still might be a bunch of stuff you want to take home. Your options are to take it with you (troublesome and expensive) or send it (still, fairly expensive). You can send boxes home either quickly with airmail or slowly (as in a month or three) via sea. Sea is a bit cheaper and a lot of this stuff you won't need immediately. Shipping a large box, within the size and weight limit can cost around ￥10,000 to ￥15,000.