Allah the All-Mighty has said,

  وَقَالَ رَبُّكُمُ ٱدْعُونِىٓ أَسْتَجِبْ لَكُمْ ۚ إِنَّ ٱلَّذِينَ يَسْتَكْبِرُونَ عَنْ عِبَادَتِى سَيَدْخُلُونَ جَهَنَّمَ دَاخِرِينَ  

Wa qaala Rabbukumud 'ooneee astajib lakum; innal lazeena yastakbiroona an 'ibaadatee sa yadkhuloona jahannama daakhireen 

And your Lord says: "Call on Me; I will answer your (Prayer): but those who are too arrogant to serve Me will surely find themselves in Hell - in humiliation!"(Quran - 40:60)

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Abu Hurayrah (ra) narrated that the Prophet (saw) said, "There is nothing that is more noble in the sight of Allah than Du'a."

(At-Tirmidhi)

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Nu'man Ibn Bashir (ra) reported that the Prophet saw said, "Du'a is worship."

(Ahmad)

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And he (saw) also said, "The best form of worship is Du'a."

(Al-Hakim)

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Abu Hurayrah (ra) narrated that the Prophet (saw) said, "Verily, the prson who does not ask Allah, Allah gets angry at him."  

(At-Tirmidhi)

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The Prophet (saw) said, "The most incapable (or lazy)person is he who does not make Du'a and the most miserly is he who does not give salam."

(Ibn-Hibban)

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The Prophet (saw) said, "Nothing repels predestination (qadr) except Du'a."

(At-Tirmidhi)

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He (pbuh) also said, "Caution will not be of any benefit against predestination, but Du'a benefits (matters) that have occurred and that are (yet) to occur. And indeed Du'a meets with a calamity and fights it until the Day of Judgement."

(At-Tabarani)