Textbooks tell you that “I” or “me” is translated by watashi (私) in Japanese. This is true, but incomplete. There are indeed a lot of words or expressions to designate the first person.
boku (僕) is used only by men, and is more familiar. But also considered as “cute” when used by young boys.
ore (俺) also exclusively masculine, is more familiar than boku, and to avoid if not wanting to be rude (however, ore is rather “cool” among young people, and more widely used by men when they are among themselves).
atashi (あたし) is a woman-only variation of watashi. It stresses the female side of who uses it.
washi (わし) is one more variation of watashi, but used by elderly men. This expression is appropriate for grizzled pappies.
watakushi (私) is a very polite expression, which can even become conceited at times. It is however commonly used at work, especially when speaking to a customer.
atakushi (あたくし) is a femal variation of watakushi
And this list is probably not complete. There are plenty of useful words like uchi or kochi (which literally mean “at home” and “over here”), which can also be used to speak of oneself. There is also wa ga hai (我が輩, like in the famous play of Natsume Sohseki, wa ga hai ha neko de aru : “I am a cat”); although nobody uses this aged expression, wa ga ya (我家) is still used to say “at my home”…
Finally, I must say that I don’t know why there are so many ways to speak of oneself in Japanese. If you have an idea, I’d be happy to hear it.