What ^ said
If you want to bring presents for the kids/teachers, do something small, like Singapore lapel/badge pins. I gave them out like candy.
If you are a senior high school ALT with a base school where you go to every day, you can also throw in one (one is more than enough unless it's a massive massive school, in which case, give it to the English dept, the VP, P and the office ladies and it'll still be enough) Bengawan Solo tin can of whatever you like. They love the stuff and the cans are pretty to them.
Edit as I go through the thread:
Smartphones vs Keitai's - Everyone in Japan is swapping to smartphones now and keitai's are on the way out. As coolass as it sounds to own a 12megapixel keitai that watches 1SEG TV on the go and has unique kisekae screens, it probably isn't worth it in the longer run (or even the short run, for the 1 year person) as many people who I personally know who bought keitai's regretted it. Also, it's much harder to sell back your keitai than a smartphone these days. Most shops offer very low return prices (I know, I checked.)
Also, for carriers - Check where you are living before you decide. Softbank is "the best" in terms of price and free calls, but it has notoriously bad signal strength away from big cities. That's not to say it will drop dead entirely, but it's highly likely you won't get things sometimes. The better bet is to look at au, which offers the best combi of price + coverage. If you don't worry about price too much, Docomo is guaranteed the best coverage all over and even in the dead of a jungle trek(!) and they usually have some of the sexiest models (You get what you pay for I guess)
You *can* bring your phone here if it works on 3G, but as mentioned getting a new contract w/o a phone alongside is usually more expensive. You could, however, hang on to it if it's, say, a smartphoone like an iPhone that can utilize Wi-Fi.
Also consider looking up English info on the various plans they have - most offer some form of data plan. I'm unsure if they ever did (or still do) offer "packethodai" or unlimited data usage for anything other than iPad's anymore - but most have more than one plan that will set your monthly price at a certain "cap" after a certain amount of data has been used. Quite useful if you think you;ll whatsapp etc alot.
You can bring whatever you want so long as it doesn't bust the limit on the plane ride over - I had a friend bring his bike while I brought my entire PC casing (Since I was unsure of picking up a custom PC in Japan at the time and didn't want to use a Japanese keyboard either) and you probably should do as much as you can. When you arrive, they will immediately ask which of your bags you want to send ahead to your placement location. You give them whichever bags you want, and off they go while you carry on to Tokyo with the hand luggage and smaller other baggage. Obviously, pack lighter for the Tokyo to placement leg because as mentioned, you may be required to lug that stuff from Place A to Place B by yourself! (I was lucky in having my school pick me up from the airport, but the dreaded ESID does apply....)
Good luck newcomers!