It is impossible to list on one page enough phrases for a reader to be able to survive in Japan alone, but here are some of the most useful phrases; some are extremely polite and others are extremely rude, so pay attention to the notes.

Don't forget to look at the pronounciation guide!

Ogenki desu ka? "How are you?" (lit. "Are you healthy?") Informal: Ogenki?
Hai, genki desu. "I'm fine." (lit. "Yes, I am healthy.") Informal: "Ee, (genki da)."
Iie, genki ja arimasen. "I'm not well." (lit. "No, I am not healthy.") Informal: "Iie, (genki ja nai)."
Watashi no namae wa _____ desu. "My name is _____." Informal: "Atashi ______." (feminine) "Boku _____ da." (masculine)
Ohayou gozaimasu. "Good morning." Informal: "Ohayou." "Ohaa." "Osu." (masculine)
Konnichi wa. "Good afternoon."
Konban wa. "Good evening."
Oyasumi nasai. "Good night." Informal: "Oyasumi."
Sou desu ka. "Is that so?" Informal: "Sou ka." (masuline)
Hajimemashite. "Nice to meet you." Informal: "Yoroshiku."
Doozo yoroshiku. "It is my pleasure." Informal: "Yoroshiku."
Kochira koso doozo yoroshiku. "It is I who should thank you for the pleasure of meeting."
Kochira wa _____ desu. "This is _____."
     chihi "my father"
     haha "my mother"
     ani "my older brother"
     ane "my older sister"
     otouto "my younger brother"
     imouto "my younger sister"
     itoko "my cousin"
     kareshi "my boyfriend"
     kanojo "my girlfriend"
Okaasan. "Mom." Also: "Kaasan." "Okaachan." "Kaachan." "Mama."
Otousan. "Dad." Also: "Tousan." "Otouchan." "Touchan." "Papa."
Oniisan. "Big bro." Also: "Niisan." "Oniichan." "Niichan."
Oneesan. "Big sis." Also: "Neesan." Oneechan." "Neechan."

Informal/Slang Phrases:
Suki yo. "I like it." Also: "Suki da." (masculine) "Suki wa yo." (feminine)
Daisuki yo. "I really like it." Also: "Daisuki da." (masculine) "Daisuki wa yo." (feminine)
Kirai yo. "I dislike it." Also: "Kirai da." (masculine) "Kirai wa yo." (feminine)
Daikirai yo. "I hate it." Also: "Daikirai da." (masculine) "Daikirai wa yo." (feminine)
(Note: in these phrases the object is implied. Therefore, depending on the conversation, they could mean "I like you," "I like him," "I like carrots," or anything else.)
Baka! "Stupid!" "Idiot!"
Yurusenai. "I won't forgive (you/it/he/she/them)."
Zutto. "Forever."

Look on the links page to find sources of more Japanese words and phrases.