Greeting another Muslim

As salamu alaykum wa Rahmatullahi wa Barakatuh.
Translation: May the peace of Allah descend upon you and His Mercy and Blessings.

When salaam is conveyed (when some conveys salam to you on another's behalf).

Alayka wa alay-his salaamu wa Rahmatullahi wa Barakatuh.
Translation: Upon you and upon him be the peace of Allah, His mercy and blessings.

Before a meal

Bismillahi wa 'ala baraka-tillah.
Translation: With Allah's name and uon the blessings granted by Allah (do we eat).

After having a meal

Alham do lillah hilla-thee At Amana wa saquana waja 'alana minal Muslimeen.
Translation: All praise is due to Allah who gave us food and drink and who made us Muslims.

Dua for ZamZam (Holy Water)

Allah humma Innee As alooka 'ilman naa fee-ow wa Rizq-ow waa See-ow wa Shee-faa amm min Kooll-lee daa-een.
Translation:  O Allah, I ask You to grant me beneficial knowledge, abundant sustenance and cure from all diseases.

Before wudhu (ablution)

Allahumma-gh fir-lee dhan-bee wawass si'lee fi dari wa bariklee fi rizq.
Translation: O Allah Forgive my sins, make my home accommodating and grant me abundance in my livelihood.

After wudhu

Allahummaj 'al-ni minat-tow-wa beena waj-alni minal muta-tah-hireen.
Translation: I testify that there is no deity except Allah; He is One and has no partner.  And I testify that Muhammad (Sallallahu alayhi wasallam) is His servant and apostle.

When entering the masjid (mosque)

A'uthu bil-Lahil 'atheemi wa biwajhi-hil kareemi wasultaani-hil qadeemi minash-shaytaanir rajeem.
Translation: I seek protection from Allah, The Sublime, and I seek the protection of His Merciful Self and of His Eternal Kingdom against the accursed devil.

After sneezing

Alhamdulillah! (right graphic) / Alhamdu lillahi 'ala kull-lee ha-leen (left graphic).
Translation: Thanks and all praise be to Allah (or) Thanks and all praise be to Allah under all conditions.

Reply to someone who sneezes

Yar Hamoo kall Lah.
Translation: May Allah have mercy on you.

When a Non-Muslim sneezes

Yahdee Kumullahu wa Yaslih Ba Lakoom. 
Translation: May Allah give you guidance and make your children pious.

When someone is critically ill
When someone is so critically ill that there is no hope for his recovery, under no circumstances should he (or she) pray for his (or her) death.  But if one must, then one should recite the following dua:

Allah-humma ah-yini ma kaanatil hayaatu khairall-lee wa tawaff-fani i-dha kaanatil wa faato khai-rall-lee.
Translation: O Allah, keep me alive so long as it is in my best interest and give me death when it is in my best interest.

When visiting the sick

La ba'sa tahoorun inshaa-Allah. La ba'sa tahoorun inshaa-Allah.
Translation: No need to worry.  It (this sickness) is a means of cleansing from sins.  No need to worry. It (this sickness) is a means of cleansing from sins.

Dua taught to a new muslim

Allahummagh fir-lee warr hamnee wah-dini warr zuq-ni.
Translation: O Allah, forgive me, have mercy on me, guide me aright and grant me sustenance.

When entering the toilet

Allahumma in-nee a'oothu bika minal khubu-thee wal khabaa ith.

When leaving the toilet, recite

Ghuf-raa naka

followed by

Alhamdulillah-hilla-thee ath-haba ann-nil athaa wa 'afaani.

Reaching the top of an incline

Allahumma lakash-sharafu 'ala kull-lee shara-few walakal hamdu 'ala kull-li haalin.
Translation: O Allah, all sublimity is for You at every incline and all praise is for You at all times under all conditions.  

Repentance dua
Whenever a person commits any sin, he/she should immediately offer repentance to Allah, saying the following dua.  

Allahumma In-nee a-toobu ilayka minha la ar-ji-u ilayhaa abada.
Translation: O Allah, I repent before You for all my sins and I promise never to return to the same (again).

Upon awakening

Alhamdulillah-hillathee ah-yana ba'da ma ama tana wa ilayhi nushoor.
Translation: Many thanks to Allah who gave us life after having given us death and (our) final return (on the Day of Qiyaamah (Judgement)) is to Him.

When undertaking a journey

Subhanalla-thee sakh-khara-lana haatha wa-ma kun-na lahoo muqrineena wa inna ila Rabbina la-mun-qali-boon.
Translation: Glory be to Him (Allah) who has brought this (vehicle) under our control though we were unable to control it.  Sure, we are to return to our Lord.

Istikhara for nikah (marriage)
When intending to marry someone then even before proposing or expressing one's intention to propose, one should perform Wudhu in the best of manner and then offer as many Nafl Salaahs as possible.  Thereafter one should praise and glorify Allah in the best manner and recite the following Dua:

Translation:  O Allah, You have power and I have none.  You know all and I know not.  You are The Knower of all that is hidden.  If, in Your knowledge (mention name of person here) be good for me in my faith and in my temporal and religious life, then ordain her (or him) for me.  And if anyone other than her (or him) be good for me in my faith and religious life, then ordain her (or him) for me.

Dua-e-Qunoot (read in Witr)

Translation: O Allah! We beg help from You alone; ask forgiveness from You alone, and turn towards You and praise You for all the good things and are grateful to You and are not ungrateful to You and we part and break off with all those who are disobedient to you. O Allah! You alone do we worship and pray exclusively to You and bow before You alone and we hasten eagerly towards You and we fear Your severe punishment and hope for Your Mercy as your severe punishment is surely to be meted out to the unbelievers.