Niyyah (formal intention):
Nawaitul hajj wa ahramtu bihi lillahi azza wa jall
I make intention for the Hajj, and have entered into ahram for the sake of Allah the Mighty, the Glorified.
Labbaik, Allahumma labbaik, labbaika la shareeka laka labbaik, innal hamda wanne'matah laka wal mulk, la shareeka laka
Here I am, O Allah! Here I am; Here I am, there is no partner unto You, Here I am; all praise and favours and sovereignty belongs to You, there is no partner unto You.
On reaching Meeqat:
Allahumma haza haramuka wa amnuka faharrimni 'alannar, wa amminnee min azabika yauma tab'asu ibadaka, waj'alnee min aulia'ika wa ahli ta'atika
O Allah this is your santuary(sacred) and protected place, so forbid me on fire, and protect me from Your punishment on the day You will raise Your servants (again) and make me from among those who are close to You and are obedient to You.
On Seeing Kaba for the fist time (also when saying farewell):
Allahumma zid hazal baita tashreefan wa ta'zeeman, wa takreeman, wa mahabatan, wa zid mun sharrafahu wa karramahu, mimmun hajjahu awi'tamarahu tashreefan wa takreeman wa tazeeman wa birran
O Allah increase this house in honor, and reverence, and respect and awe. And whosoever venerates and honors this house, coming to it for Hajj or Umrah, increase (him/her) in position, respect, honor and righteousness.
Starting Tawaf at Hijr-al-aswad (and each shawt):
Bismillahi Allahu akbar, allahumma imanan bika wa tasdeeqan bikitabika wa wafa'an bi ahdika wa ittiba'an lisunnati nabiyyika sallallahu alaihi wasallam
In the name of Allah, and Allah is the greatest. O Allah, with faith in You and testifying to the truthfulness of Your Book, and in fulfilling our covenant with You, and following the sunnah of your prophet, may your blessings and peace be upon him.
Tawaf/Arafah and other times:
Subhanallah, walhamdulillah, wala ilaha illallah, wallahu akbar, wala hawla wala quwwata illa billah
Glory be to Allah, All praise is to Allah, there is no god but Allah. There is no power and no strength except in Allah.
Towards end of each round and at other times:
Allahumma rabbana aatina fidduniya hasanah wa fil aakhirati hasanah wa qina azaban nar
O Allah, our Lord, give us good in this world, and good in the Hereafter, and save us from the punishment of fire.
Tawaf/Saee/Arafah and other times:
Allahu akbar Allahu akbar Allahu akbar wa lillahil hamd, la ilaha illallahu wahdahu la shareeka lahu lahul mulk wa lahul hamd yuhee wa yumeet biyadihil khayr wa huwa ala kulli shai'n qadeer.
Allah is the greatest, Allah is the greatest, Allah is the greatest, to Allah is all praise. There is no god but Allah, He is One and has no partner. To Him belongs all praise and sovereignty. He gives life and takes it away. In His hands is all that is good and He is powerful over everything.
At all times:
Allahumma jalhu hajjan mabrooran wa zanban maghfooran wa sa'ian mashkooran
O Allah, make this a blessed Hajj, with sins forgiven and effort that is accepted.