Not at all. 1. There are lots of ways to say "I": 私、僕、俺、あたし。。。 2. In Japanese these are often omitted if their presence is clear by the context.

Keep in mind that in Japanese, subjects of the sentence are dropped very very often. If it's obvious, they won't say it. You can have a complete sentence with only a verb. 95ferortiz mentions this. I think it's more common to drop it, than to include it. Also, what version of "I" the speaker chooses depends a lot on context. 私 is common in the right context, usually a little bit more formal places like work when talking to customers. A young woman might call herself あたし to her friends but then use 私 while at work. I did a quick hunt through my emails to see what my Japanese coworkers use. The vast majority of the time there is no use of any "I", when I did find one, it was 私.