Key Haji dhikr includes the Talbiyah (from ihram to stoning), the Arafah declaration of tawheed, takbirat al-Tashreeq on the 11th-13th, and personal doa during tawaf.
Dhikr (remembrance of Allah) is the spiritual essence of Haji, transforming physical actions into acts of deep worship. The most important dhikr during Haji is the Talbiyah: 'Labbayk Allahumma labbayk, labbayk la sharika laka labbayk, innal hamda wan-ni'mata laka wal-mulk, la sharika lak.' This should be recited frequently and aloud (for men) from the moment of entering ihram until the stoning of Jamarat al-Aqaba on the 10th.
At Arafah, Nabi (shallallahu alaihi wa sallam) said: 'The best doa is on the Day of Arafah, and the best thing that I and the prophets before me said is: La ilaha illa Allahu wahdahu la sharika lah, lahul mulku wa lahul hamdu wa huwa ala kulli shay'in qadir.' During the days of Tashreeq (11th-13th), the takbirat of Tashreeq are prescribed: 'Allahu Akbar, Allahu Akbar, la ilaha illa Allah, Allahu Akbar, Allahu Akbar, wa lillahil hamd.' During tawaf, there is no specific prescribed dhikr — scholars advise making personal doa, reciting Al-Quran, or any dhikr that moves your heart. Between the Yemeni corner and the Hajar Aswad, the sunnah doa is: 'Rabbana atina fid-dunya hasanah wa fil-akhirati hasanah waqina adhab al-nar.'
Source: Sunan al-Tirmidhi; Muwatta of Imam Malik; Sahih Muslim