Dua is at the core of our worship and the Noble Quran and Hadith greatly emphasize it.
وَإِذَا سَأَلَكَ عِبَادِي عَنِّي فَإِنِّي قَرِيبٌ أُجِيبُ دَعْوَةَ الدَّاعِ إِذَا دَعَانِ فَلْيَسْتَجِيبُوا لِي وَلْيُؤْمِنُوا بِي لَعَلَّهُمْ يَرْشُدُونَ
And when My slaves ask you (O Muhammad s.a.w.) concerning Me, then (answer them), I am indeed near (to them by My Knowledge). I respond to the invocations of the supplicant when he calls on Me (without any mediator or intercessor). So let them obey Me and believe in Me, so that they may be on the right path.” (Surah Al-Baqarah, 2:186)

It is not surprising then that the Holy Prophet ﷺ was pleased to have said:
وعن النعمان بن بشير رضي الله عنهما عن النبي صلى الله عليه وسلم قال‏:‏ ‏ الدعاء هو العبادة‏
An-Nu’man bin Bashir RA reported: The Prophet (ﷺ) said, “Du’a (supplication) is worship.” [Abu Dawud].

At the core of Dua or supplicating to Allah, is the humility and humbleness that the servant of Allah shows before his Lord. In everything that the Messenger of Allah ﷺ did he always displayed his humility, even when he ate, he sat like how a slave would sit and showed that he was in need of the food and not the food in need of him. And who could be more humble or who could be more eager to show his humility before Allah than the Prophet ﷺ. Therefore Nabi ﷺ loved engaging in Dua and humbling himself before his Lord.

The incident at Taif is an amazing display of the Prophet ﷺ `s love for Dua.

After a decade of preaching in Makkah, the Prophet ﷺ had lost his uncle and his wife and was still rejected by his people. In an attempt to find a more receptive audience, the Prophet ﷺ travelled to Taif, hoping that his message would find a home in the oasis city. Instead, he was rudely insulted by the city leaders and then pelted with stones by the inhabitants. Bruised and rejected, with his blood clotting as it leaked onto his shoes, he made his way out of the town. When he was safe from the mob who had pelted him, what was the first thing the Prophet ﷺ did? He didn’t go in search of a doctor to tend to his wounds, he didn’t search for food or water to satiate his hunger or quench his thirst, the first thing the Messenger of Allah ﷺ did was he turned to Allah in supplication, where he offered those rendering words, blaming himself for the people not accepting his message and pleading with Allah for His pleasure.

The most common duas of the Prophet ﷺ was:
وعن عائشة، رضي الله عنها، قالت‏:‏ كان رسول الله صلى الله عليه وسلم، يستحب الجوامع من الدعاء، ويدع ما سوى ذلك‏.‏
‘Aishah RA reported: The Messenger of Allah (ﷺ) liked comprehensive supplications or (Al-Jawami’ – i.e., supplications with very few words but comprehensive in meanings), and discarded others. [Abu Dawud].
وعن أنس رضي الله عنه، قال‏:‏ كان أكثر دعاء النبي صلى الله عليه وسلم‏:‏ ‏
‏اللهم آتنا في الدنيا حسنة، وفي الآخرة حسنة، وقنا عذاب النار
Hadhrat Anas RA reported: The supplication most often recited by the Prophet (ﷺ) was: (O our Rubb! give us in this world that which is good and in the Hereafter that which is good, and save us from the punishment of the Fire).”‘ [Al-Bukhari and Muslim].

In the narration of Muslim it is added that whenever Hadhrat Anas RA supplicated, he used to beseech Allah with this Du’a.
وعن ابن مسعود، رضي الله عنه، أن النبي، صلى الله عليه وسلم، كان يقول‏:‏ ‏ ‏اللهم إني أسألك الهدى، والتقى، والعفاف، والغنى‏
Hadhrat Abdullah bin Mas’ud RA reported: The Prophet (ﷺ) used to supplicate: “Allahumma inni as’alukal-huda, wat-tuqa, wal-‘afafa, wal-ghina (O Allah! I beseech You for guidance, piety, chastity and contentment).” [Muslim].

وعن طارق بن أشيم، رضي الله عنه، قال‏:‏ كان الرجل إذا أسلم علمه النبي صلى الله عليه وسلم، الصلاة، ثم أمره أن يدعو بهؤلاء الكلمات‏:‏ ‏‏اللهم اغفر لي، وارحمني، واهدني، وعافني، وارزقني‏
Hadhrat Tariq bin Ashyam RA reported: Whenever a man entered the fold of Islam, the Prophet (ﷺ) would show him how to perform Salat and then direct him to supplicate: O Allah! Forgive me, have mercy on me, guide me, guard me against harm and provide me with sustenance and salvation.”‘ [Muslim].

In another narration Tariq said: A man came to the Prophet (ﷺ) and said to him: “O Messenger of Allah! What shall I say if I want to pray to my Rubb?” He (ﷺ) said, “Say: ‘Allahumma-ghfir li, warhamni, wa ‘afini, warzuqni (O Allah! Forgive me, have mercy on me, protect me and provide me with sustenance).’ Surely, this supplication is better for you in this life and in the Hereafter.”