Here are a bunch of phrases, with the typos fixed from previous writeups:

Common Phrases:
Thank You - Spasibo
Please/You're Welcome - Pozhalusta
Hi - Privet
Hello - Zdrastvuyte
Bye - Poka*
Goodbye - Do Svedanya (lit. till we meet)
Good Morning - Dobroyo Utro
Good Day - Dobriy Den'
Good Evening - Dobriy Vecher
Good Night - Spokoyniy Nochi

Things:
Pen - Ruchka
Pencil - Korondash*
Cow - korova*
Chicken - kuritza
Car - Mashina
House - Dom

Useful/Not So Useful Phrases:
Help! My car is on fire! - Pomogite*! Moya* mashina gorit*!
Someone wants to kill me! - Kto-to hochet menya ubit'!
Do you have any vodka? - U vas est' vodka?
I am a silly American, please do not rob me. - Ya glupiy amerikanetz, pozhaluysta ne obvaruyte menya.
I hate this country! - Ya nenavizhu etu stranu!
You are all communists! - Vi vse kommunisti!
It's very cold here. - Tut ochen holodno.
Give me a sweater. - Day mne koftu.
Help! I've got dollars! - Pomogite*! U menya est' dolari!
Where is the nearest bathroom? - Gde blizhayshiy tualet?
That's really far away! - Eto ochen daleko!
How do I get there? - Kak mne tuda popast'?
Wow, vodka is cheap here! - Wow, vodka ochen deshovaya tut!
To boldy go where no man has gone before. - Idti smelo tuda kuda nekto eshe ne poshel.
Today is a good day to die. - Sevodnya horoshiy den' umeret'.
Mary had a little lamb. - U Mary bila malenkaya ovtza.
Where can I buy tickets to get out of this frozen hell? - Gde ya mogu kupit' bileti shtob vibratsa iz etovo zamerzhshovo ada?
The end. - Konetz.

* These words are often pronounced with an 'a' sound for the 'o', e.g. poka is pronounced paka, this is true in southern regions of Russia, e.g. Moscow.