In modern Japanese there are 8 1st personal pronouns: watakushi, atakushi, watashi, atashi, washi, boku, ore, jibun, although atakushi, washi and jibun are becoming old-fashioned.
The first person pronouns (e.g. watashi, 私) and second person pronouns (e.g. anata, 貴方) are certainly used in formal situations. In many sentences, when an English speaker would use the pronouns "I" and "you", they are omitted in Japanese. Personal pronouns can sure be left out when it is clear who the speaker is talking about.
Some Japanese personal pronouns:
Romaji - Hiragana - Kanji - Level of speech - Gender - Notes
watashi わたし 私 formal/informal all In formal or polite contexts, this is gender neutral; in casual speech, it is typically only used by women. Use by men in casual contexts may be perceived as stiff.
watakushi わたくし 私 very formal all The most formal personal pronoun. Outdated curriculums did not provide for any other kind of pronoun in everyday speech for foreigners, except for watakushi. But in modern student books, such a pronoun has been withdrawn from use.
ware われ 我, 吾 very formal all Used in literary style writing. Also used as rude second person in western dialects.
waga わが 我が very formal all Means "my" or "our". Used in speeches and formalities; 我が社 waga-sha (our company) or 我が国 waga-kuni (our country).
ore おれ 俺 informal males Frequently used by men. Establishes a sense of "masculinity". Can be seen as rude depending on the context. Emphasizes one's own status when used with peers and with those who are younger or of lesser status. Among close friends or family, its use conveys familiarity rather than "masculinity" or superiority. It was used also by women until the late Edo period and still is in some dialects. Also oi in Kyushu dialect.