The Prophet ﷺ did Ramal in (first) three rounds (of Tawaf), and walked in the remaining four, in Hajj and Umra.  

سَعَى النَّبِيُّ ﷺ ثَلاَثَةَ أَشْوَاطٍ وَمَشَى أَرْبَعَةً فِي الْحَجِّ وَالْعُمْرَةِ  

"ʿUmar bin Al-Khattab addressed the Corner (Black Stone) saying, 'By Allah! I know that you are a stone and can neither benefit nor harm. Had I not seen the Prophet ﷺ touching (and kissing) you, I would never have touched (and kissed) you.' Then he kissed it and said, 'There is no reason for us to do Ramal (in Tawaf) except that we wanted to show off before the pagans, and now Allah has destroyed them.' ʿUmar added, '(Nevertheless), the Prophet ﷺ did that and we do not want to leave it (i.e. Ramal).'  

لِلرُّكْنِ أَمَا وَاللَّهِ إِنِّي لأَعْلَمُ أَنَّكَ حَجَرٌ لاَ تَضُرُّ وَلاَ تَنْفَعُ وَلَوْلاَ أَنِّي رَأَيْتُ النَّبِيَّ ﷺ اسْتَلَمَكَ مَا اسْتَلَمْتُكَ فَاسْتَلَمَهُ ثُمَّ قَالَ فَمَا لَنَا وَلِلرَّمَلِ إِنَّمَا كُنَّا رَاءَيْنَا بِهِ الْمُشْرِكِينَ وَقَدْ أَهْلَكَهُمُ اللَّهُ ثُمَّ قَالَ شَىْءٌ صَنَعَهُ النَّبِيُّ ﷺ فَلاَ نُحِبُّ أَنْ نَتْرُكَهُ  

Ibn ʿUmar. said, "I have never missed the touching of these two stones of Kaʿba (the Black Stone and the Yemenite Corner) both in the presence and the absence of crowds, since I saw the Prophet ﷺ touching them." I asked Nafiʿ: "Did Ibn ʿUmar use to walk between the two Corners?" Nafiʿ replied, "He used to walk in order that it might be easy for him to touch it (the Corner Stone)."  

مَا تَرَكْتُ اسْتِلاَمَ هَذَيْنِ الرُّكْنَيْنِ فِي شِدَّةٍ وَلاَ رَخَاءٍ مُنْذُ رَأَيْتُ النَّبِيَّ ﷺ يَسْتَلِمُهُمَا قُلْتُ لِنَافِعٍ أَكَانَ ابْنُ عُمَرَ يَمْشِي بَيْنَ الرُّكْنَيْنِ قَالَ إِنَّمَا كَانَ يَمْشِي لِيَكُونَ أَيْسَرَ لاِسْتِلاَمِهِ