When is the Night of Al-Qadr?
The Night of Al-Qadr occurs in the last ten nights of Ramadaan during an odd night (i.e. 21st, 23rd, 25th, 27th or 29th). However the scholars differ as to if it is fixed to one of these odd nights every year or if it changes every year to a different odd-numbered night. Below are the sayings of two of our great scholars, Muhammad Ibn Saalih Al-'Uthaimeen and Muhammad Naasir-ud-Deen Al-Albaanee (may Allaah have mercy on both of them).
The Night of Al-Qadr has a Fixed Date:
The best night in Ramadaan is the Night of Al-Qadr, based on the Prophet's saying: "Whoever performs the night prayer on the Night of Al-Qadr with firm faith and while seeking reward, his past sins will be forgiven." 
It is on the twenty-seventh night of Ramadaan according to the strongest opinion. A majority of the ahaadeeth comply with this, including the hadeeth of Zurr Ibn Hubaysh who said: "I heard Ubay Bin Ka'ab (raa) say when it was said to him that 'Abdullaah Ibn Mas'ood (raa) said "Whoever performs the night prayer (every night) throughout the year will achieve the Night of Al-Qadr." He (Ubay Bin Ka'ab) said: "May Allaah have mercy on him, his intention was that the people not (grow lazy) and depend solely (on just one night). By the One of whom there is no deity worthy of worship beside Him, it is indeed in Ramadaan. And by Allaah I know on which night it is. It is on the night that Allaah's Messenger (saws) commanded us to perform the Night Prayer. It is on the twenty-seventh night. Its sign is that the sun rises on its following morning bright with no rays."
In one report this is raised to being a saying of the Prophet (saws). 
[Imaam Al-Albaanee in his book Qiyaam Ramadaan (pg. 18-19)]
The Night of Al-Qadr is to be sought:
The Night of Al-Qadr is in the last ten nights of Ramadaan, based on the saying of the Prophet (saws): "Search for the Night of Al-Qadr in the last ten nights of Ramadaan." [Al-Bukhaaree and Muslim] And it falls in one of the odd nights more likely than on the even nights, based on the Prophet's (saws) saying: "Search for the Night of Al-Qadr in the odd nights of the last ten nights of Ramadaan." [Al-Bukhaaree] And it is closer to the last seven nights, based on the hadeeth of Ibn 'Umar (raa) that: "Some men from the Companions of Allaah's Messenger (saws) saw the Night of Al-Qadr in a dream during the last seven nights (of Ramadaan). So the Prophet (saws) said: 'I see that all of your dreams agree that it (the Night of Al-Qadr) is in the last seven nights. So whoever wants to search for it, then let him search for it in the last seven nights.'" [Al-Bukhaaree and Muslim] And it is also based on the hadeeth in Muslim from Ibn 'Umar (raa) that the Prophet (saws) said: "Look for it in the last ten nights. But if one of you becomes weak or is unable, then do not let the remaining (last) seven nights overcome him."
Amongst the odd nights in the last seven nights, it is closest to the twenty-seventh night due to the hadeeth of Ubay Bin Ka'ab (raa) who said: "By Allaah, I know which night it is. It is on the night that Allaah's Messenger (saws) commanded us to perform the Night Prayer. It is on the twenty-seventh night." [Muslim]
The Night of Al-Qadr is not specified to one fixed night throughout all the years. Rather, it constantly changes. So one year it could occur on the twenty-seventh night for example and on another year it could occur on the twenty-fifth night, according to Allaah's Will and Wisdom. What directs us to this is the Prophet's (saws) saying: "Look for it (i.e. the Night of Al-Qadr) when there remain nine nights, when there remains seven nights, or when there remains five nights (i.e. 21st, 23rd, and 25th respectively without mention of 27th)."
Al-Haafidh Ibn Hajr said in Fath-ul-Baaree: "The most strongest opinion is that it is on an odd night in the last ten nights and that it constantly changes."
Allaah has hidden knowledge of its occurrence from His servants out of mercy for them so that they can increase their actions in the search for it during these honorable nights, by praying, making dhikr and supplicating. So they grow and increase in the nearness to Allaah and His reward. And He also kept it hidden from them as a test for them to distinguish who amongst them struggles and makes an effort to find it and who is lazy and negligent. This is since whoever constantly strives for something, he will exert himself in his search for it and trouble himself in finding it and achieving it.
And perhaps Allaah discloses the time of its occurrence to some of His servants through signs and signals, which one is able to see, just as the Prophet (saws) saw its sign that he would be prostrating in mud on its following morning. So it rained on that night and he prayed the (following) morning (Fajr) prayer in mud.
[Imaam Muhammad Ibn Saalih Al-'Uthaimeen in his book Majaalis Shahr Ramadaan (pg. 106-107)]
 Reported by Al-Bukhaaree, Muslim and others from the narration of Abu Hurairah (raa) and by Ahmad (5/318) from the narration of 'Ubaadah Ibn As-Saamit (raa). The addition to it in [...] belongs to him and to Muslim from Abu Hurairah.
 Reported by Muslim and others and it is referenced in Saheeh Abee Dawood (1247)