There are many words that we can use in place of わたし depending on who we are or how we perceive ourselves, whom we are talking to, and so on. Some of my observations (which may not hold true all of the time) are as follows.
Young boys use 僕 （ぼく）. Interestingly I once heard a very young girl use this word.
Young men often use 俺 （おれ） in friendly conversation. When I asked my high school students last year, they told me that I should use おれ. I should mention that I’m 24 years old. Another student said that it sounded funny when I used it which now surprises me even more as I have heard numerous elementary school children using おれ to refer to themselves!
Often young men seem to change from おれ to 僕 （ぼく） when talking to someone ‘above’ them (e.g. a parent’s friend).
This change can become permanent or after the man ages a little and doesn’t feel おれ is suitable any longer.
Older men can use different words such as わし and so on, but I have only ever heard these words in anime and in film subtitles – do people really use these in Japan these days?
For girls, a common replacement for わたし is あたし.
Interestingly, a friend from Kyoto told me that both boys and girls can use うち for わたし (bearing in mind うち is often used to refer to one’s home).
Then there are the formal personal prounounds such as わたし and the super-polite わたくし. One guy I was talking to said he has to use わたくし in his job interviews. At the time he was a final year university student looking for his first full-time job.