Allah
Arabic word for God

Al-hamdu lillah 
"Praise be to Allah"
Recited when praising Allah, said upon any occasion of joy, acceptance of an occurrence good or bad. It's also a response to 'How are you?'. Its meaning is very broad and it denotes giving thanks to Allah as well as reaffirming that He Alone is to be praised for all that occurs.

Bismillah ar-Rahman ar-Rahim
"In the name of Allah, the Most Beneficent, the Most Merciful."
Recite before any activity

A'uzu Billahi Minashaitanir Rajim
"I seek refuge from Allah from the accursed devil."
Recite before doing anything [extended version of above]

Allahu Akbar
"Allah is the Greatest"
To praise Allah in every aspect of life

La Ilaha Illallah
"There is no God except Allah."
Part of the first pillar of Islam,
also one of the best forms of dhikr [remembrance]

Assalamu Alaikum
"Peace be upon you"
Universal greeting for the Muslims

Wa 'Alaikumus Salam
"And upon you is the peace"
Response to previous greeting

Assalamu Alaikum wa Rahmatullahi wa Barakatuh 
"Peace and the Mercy and Blessings of God be upon you" 
Extended form of assalamu alaikum

Wassalaam
"And peace" 
used when leaving/departing from someone

Allahu Alam
"Allah Knows (best)"

Subhanahu Wa Ta'ala (S.W.T)
Allah is free of any defects or shortcomings and is to be glorified and praised. The second word is actually a verb that signifies that Allah is high above His creation in every aspect.
used when the name of Allah is written or pronounced [used only in reference to Allah]

La Hawla Wa La Quwwata Illa Billah
"There is no power and no strength save in Allah."
Putting all trust in Allah, even when the
greatest distress has come onto you

P.B.U.H 'Alaihis Salam
"peace be upon him"
An invocation of security and sanctity said on behalf of the Prophets and Messengers of Allah and the Angels that is said when hearing their names mentioned.

Sallallahu 'alaihi wa sallam (SAWS)
This is a supplication to Allah that He exalt the mention of Muhammad to the high angels and that the angels in turn praise Muhammad before Allah. This is an invocation that should be said upon mentioning or hearing the name of the Prophet Muhammad. 

In Sha' Allah
"If Allah wills"
When planning or pledging for the future,
you are doing so with the permission of Allah

Bi'idhnillah
"With Allah's Permission"
similar to previous 

Ma Sha' Allah
"What Allah has willed!"
 (Usually used to express admiration of Allah's creation)

Subhaan'Allah
"Glory be to Allah"
Allah is free of any type of defect, imperfection, or shortcoming.

Barakallahu feek
"May the blessings of Allah (be upon you)."
Thanking one another

Astaghfir Allah
"I seek forgiveness from Allah"
say when repenting 

Fi-sabil-Allah
"In the way of Allah"
Frequently used expression in the Qur'an, which
emphasizes that good acts should be done exclusively
to please Allah

Fi-Amaan-Allah
"May you be in the protection of Allah"
When parting from someone

Jazak Allahu Khairan
"May Allah reward you with good"
One says this as a prayer to Allah when showing thanks to another Muslim after he performs a righteous or good deed. (often used instead of "Thank you") 

Wa iyyakum
"And you too"
response to 'jazak Allahu khairan'

Radiallahu 'anhu
"Allah be pleased with him"
Usually said in deference to the companions of the Prophet Muhammad sallallahu 'alaihi wa sallam upon hearing their names mentioned in recognition of the favor that Allah has bestowed upon them as the fore bearers of the Islamic message. Sometimes rendered (ra) or (raa) pl. 'anhum , fem. 'anhaa , du. 'anhumaa 

Rahimahullah
 "Allah have mercy upon him"
Said when remembering a deceased Muslim. 
fem. rahimahallah also Allahu yarhamuhu or yarhamuhaa 

Ameen
"May Allah Accept"
When participating in prayer,
when someone supplicates

Ya-Allah
"Oh, Allah"
calling upon Allah 

Na-uzu-billah 
I seek refuge with Allah
When unpleasantness occurs

Tawak-kalto-al-Allah
"Have trust in Allah"
When a problem appears

Yar-hamok-Allah
"Allah have mercy on you"
Say this when someone else sneezes, after
you hear them say "Alhamdulillah"

Lihub-bullah
"For the love of Allah"
When having love for someone

Inna Lillahi Wa Inna Ilahi Raji'un
"We are from Allah and to whom we are returning."
When struck by distress or news of a death

Jihad
Striving/Struggle for Islam, (NOT holy war!)