...

(Bearing in mind that one can make dua at any time and in any place; however, the following are the most preferable times, conditions and places.)

1. Lailatul Qadr
2. Deep in the last third of the night
3. Immediately after the mandatory prayers
4. Between the adhan and iqamah
5. An hour during every night -- [hadith states that Allah comes down to the sky of the earth during the last 3rd of the night and hears the duas of the believers]
6. At the time of the call to the mandatory prayers
7. At the time of rain
8. During jihad when the ranks of fighters (mujahidoun) advance in the path of Allah
9. An hour every Friday -- the soundest opinion regarding this hour is the last hour between the hours of Asr on the day of Juma, and it could be the hour of the khutba and salat.
10. At the time of drinking Zamzam water with true intentions
11. During sajda
12. At the time of waking up at night and there are hadith regarding what the Prophet r said in these duas
13. If you sleep after having made wudu then wake up at night and then make supplication
14. After you say dua Yunus, make your personal dua or one from Qur'an or sunnah and it is La illah ila Allah subhannaka inni kuntu min al thaalimeen.
15. Dua of people after the death of a person (e.g. the dua of a person who is praying for someone who has just died)
16. Dua after praising Allah and giving salat on the Prophet (SAW) in the tashah-hud at the end of salat. Make your dua before the 2 tasleems.
17. At the time of dua, call upon Allah by the greatest of His names that, if called by them, He answers, and if asked by them, He gives (e.g. Ya Rahman, Ya Raheem, Ya Thal Jalaali wal Ikraam, Ya Al Ahad As Samad, lam yalid wa lam yulad wa lam yakum kuf wan ahad)
18. The dua of a Muslim for his brother or sister Muslim stemming from the heart.
19. Dua on the Day of Arafat
20. Dua during the month of Ramadan
21. Dua at the time of a Muslim gathering for the purpose of remembering Allah.
22. Dua at the time of a crisis by saying Inna lilahi wa inna ilaihi raje'oon, Allahuma ajurni fi museebati, wa akhlif li khairun minha. Verily, we belong to Allah, and verily, to Him is our return. O Allah, Bless me in my problem and replace it for me with something better than it.
23. Dua when the heart reaches out to Allah and is ready to be totally sincere
24. Dua of the oppressed against the one who is oppressing him
25. Dua of the father or mother for or against the son
26. Dua of the traveler
27. Dua of the one fasting until he breaks his fast.
28. Dua of the one fasting at the time of breaking fast
29. Dua of a desperate person
30. Dua of a just Imam
31. Dua of a son or daughter obedient to his or her parents
32. Dua immediately after wudu saying what has been mentioned in the hadith that is directly related to it (ablution)
33. Dua after stoning the small Shaitan (jamrat sugra) during Hajj
34. Dua after stoning the middle Shaitan (jamrat wusta) during Hajj.
35. Dua made inside the Ka'aba and the dua of one who prays inside the hijr as it is part of the house (bait Allah). [This is the semicircle to the right of the Ka'aba if you face the door.]
36. Dua on the mount of Safa during Umrah or Hajj
37. Dua on the mount of Marwa during Umrah or Hajj
38. Dua at any of the holy sites.

Note: The believer can call to his Lord at any time, wherever he is but these times and conditions and places are special and more care should be taken. Note: All of these circumstances are substantiated by hadith.