Hello
Ohayō (good morning) - informal
Ohayō gozaimasu - polite
Konnichi wa (good afternoon/good day) - general: no polite form
Komban wa (good evening) - general: no polite form
Mosh moshi - special for the telephone (but not advisable if that's the limit of your Japanese!

Goodbye
Dewa mata (see you) - "Ja mata" or "Ja ne" are more informal.
Oyasuminasai (goodnight)

Thank you
Arigatō (informal)
Arigatō gozaimasu (polite, ie. to a superior)
Arigatō gozaimashita (general for something which has been or will be done)
Sumimasen - literally "sorry", but often used in the sense of "Thank you for doing me that favour, and sorry to bother you."

Pleased to meet you
Hajimemashite - literally "it's the first time to meet".
A handshake is suitable. See etiquette.

Is there someone who can speak Engish?
Eigo no dekiru hito wa imasuka?

(That was) delicious!
Oishī! - as in many Japanese situations, one word can say it all.
If it wasn't delicious, the negative is oishiikunai, but of course that's not polite.

I'm going (out)
Ittekimasu (to which the response might be iterashai)

I'm back (home)
Tadaima! (to which the response is: o-kaeri or o-kaerinasai)

Yes
Hai! - often used in the sense of "OK, I'll do that!" With a question intonation, it can mean "Sorry, I didn't hear or understand you."
Sō desu - in the sense of "Yes, that's correct".

No
īe - but only in moderation. No-one likes to say no, as directly as that. Normally the negative form of a sentence would be used. Often used when accepting compliments or thanks (ie. in the sense of "No, it was nothing/no trouble")

What's this? Kore wa nani?

You're welcome: Dō itashimashte

Excuse me: Sumimasen

I'm sorry: Gomen nasai

Please
dōzo (when offering something)
onegai shimasu (when requesting something)

Just a moment please: Chotto matte kudasai

Please write it down: Sore o kaite kudasai

- isn't it?
desu ne? This is a general phrase which can usefully be applied in many situations, and like "n'est-ce pas?" in French, the form doesn't change:
Sō desu ne? (That's right, isn't it?)
Samui desu ne? (It's cold, isn't it?)
Atsui desu ne? (Hot, isn't it?)
Kawaii desu ne? (Sweet/cute, isn't it?)

Transportation

I lost my ticket: kippu o nakushimashta
(Show an address) Go to this address please: Koko e itte kudasai
Does this train/bus stop at ____? Kono basu/densha wa ____ ni tomarimasuka?

At the hotel/inn

Can I see the room? Heya o misete kudasai
I left my key in my room: Kagi o heya ni wasuremashta
Could you call me a taxi, please? Takushi o yonde kudasai