The Japanese prefer personal seals (sometimes they are called inkan, other times they are called hanko - I'm not sure why the two names) over what they feel are easy-to-forge signatures. There is some flexibility for gaijin on this matter, though. You can establish a bank account, a cellphone contract, even a lease with your signature, but there's a caveat:
If you start an account with an inkan/hanko, you are forever bound to using that same stamp for the term of your account (no signing one month and stamping another), so don't lose your inkan!
You can buy inkan in many places and there are inkan stores that will make a seal to your specifications, typically in less than a week. It seems that if yours is a Western name, it's likely you will get an inkan that is in romaji (the alphabet), I am guessing that all others will have their names transliterated into katakana (the Japanese syllabary). Here are some examples of inkans/hankos:
This is from the ANA Visa people and it's the organization's official seal.
This is from the Roshi (Abbot), Fukushima, of the Tofukuji monastery there are several seals on this fan.
You should only use your inkan for official documents, don't go slapping it on any old thing (which was my first impulse). For that, you use an unofficial stamp (again you can buy these all over the place), they are called sanmonban. You use sanmonban for signing for packages, maybe as a neat little embellishment to a letter to your buddies back home, whatever.
Here's an informal stamp that I use:
It says "Po-Ru" which is the transliteration into katakana of my name.
To register your inkan you must go to City Hall (near Koza here in Okinawa City) and present your gaijin card and pay some money. In Okinawa City you receive a Hibiscus Card (like a credit card) which is used to further verify your address. Here's where in City Hall you go to register (also the same window to get a gaijin card, by the way):
You go to the window there, don't worry, they speak English, and tell them what you'd like to do. They will ask for your identification and Hibiscus Card and then tell you how many tickets to purchase:
I guess it wouldn't be right to give the municipal authorities money outright, so they have this ticket system in place. You put your money into a vending machine next to the window and select the tickets you want and then present the tickets you've purchased to the office clerks. You'll notice that you rarely just put money into someone's hands in Japan.