There are many verses in Quran showing the value of dua and ordering us to use dua always. for example:
قُلْ مَا يَعْبَأُ بِكُمْ رَبِّي لَوْلَا دُعَاؤُكُمْ فَقَدْ
كَذَّبْتُمْ فَسَوْفَ يَكُونُ لِزَامًا
Say, "What would my Lord care for you if not for your supplication?"
For you have denied, so your denial is going to be
وَقَالَ رَبُّكُمُ ادْعُونِي أَسْتَجِبْ لَكُمْ إِنَّ الَّذِينَ
يَسْتَكْبِرُونَ عَنْ عِبَادَتِي سَيَدْخُلُونَ جَهَنَّمَ دَاخِرِينَ
And your Lord says, "Call upon Me; I will respond to you." Indeed,
those who disdain My worship will enter Hell [rendered] contemptible.
and other verses. also prophet SAW said: Dua is weapon of believer.
There have been many cases that real believers by only dua have immediately killed a cruel King who bother them.
Mafatih-al-jinan is a great collection from different sources. Duas.org is a great online collection with English translations of them.
Sahifa-e-Sajjadiya is called "the sister of Quran" and contains wonderful supplications and shia scholars consider it a great resource for secret knowledge and procedures of knowing and meeting God. some of sunni scholars wondered when received this book as gift and were sad that why did not know such a valuable book earlier in their life. Also some churches use parts of wonderful supplications of this book.