"I happened to pray one night with the Prophet . The Prophet started reciting al-Baqarah chapter of the Quran and I thought he would stop after 100 verses. But when he went beyond it I thought that he may want to recite the whole chapter in one Rakah. When he finished al-Baqarah I thought he would do Ruku but then he immediately started reciting al-Imran and when he finished he started reciting an-Nisa. The Prophet was reciting very slowly with enough pauses and would do Tasbih (praising God) and Dua (supplication) according to the subject being discussed in the relevant Ayah. After that the Prophet did Ruku (bowomg). In Ruku he stayed as long as he did when he was in Qiyam (standing in prayer). After Ruku he stood up for almost same time and then he performed Sajdah (prostration) and stayed there as long as he recited Quran while doing Qiyam".  (Hudaifa narrated this hadith as in Sahih al Muslim, Nasai)

Of course, not all the Prayers of the Prophet were this long. In public he would pray for a shorter period of time and ask other imams to do the same. The Prophet use to make dua in Sajdah not just tasbeeh as we do in obligatory prayers. He used to cry in Sajdah. He would spend an extended amount of his time in Sajdah whenever he was praying on his own. Many times, however, Muslims would join him when they found him praying alone.

Aisha mentions that: 

One of the Prophet's companion, Abdullah ibn Zubayr, would pray with such concentration that when he was in Sajdah the sparrows would come flying and sit on his back. In a separate narration, Abdullah ibn Abbas, another companion, said if you want to see how the Prophet of God used to pray, you should copy how Abdullah ibn Zubayr used to pray.

And consider these two Hadiths from the Sahih Muslim:

    Ma'dan b. Talha reported: 

    In the second Hadith, Rabi'a b. Ka'b said: 

Sajdah is truly a humbling experience. We can beg for God's forgiveness and cry by thinking about our misdeeds, as well as seek refuge in God from the Hellfire. We are in one of the most submissive physical positions when in Sajdah. It is one of the best occasions to ask God for forgiveness, guidance, and all that we want. It is one of the best positions in which to talk to God. Seeking God's pleasure and forgiveness need to be given top priority in these remaining days and nights of Ramadan.

Source: SoundVision - Abdul Malik Mujahid