When beginning the fast – Suhur (sehri)
وَبِصَوْمِ غَدٍ نَّوَيْتَ مِنْ شَهْرِ رَمَضَانَ
I intend to keep the fast for tomorrow in the month of Ramadan
[Abu Dawud]
Transliteration:
Wa bi-sawmi ghadin nawaytu min shahri ramadan

When breaking the fast – Iftar
اللَّهُمَّ اِنِّى لَكَ صُمْتُ وَبِكَ امنْتُ [وَعَلَيْكَ تَوَكَّلْتُ] وَعَلَى رِزْقِكَ اَفْطَرْتُ
O Allah! I fasted for You and I believe in You [and I put my trust in You] and I break my fast with Your sustenance.
["wa ‘alayka tawakkaltu" is quoted in some books of knowledge - but not all, [...]

On the authority of Anas (may Allah be pleased with him): The Messenger of Allah (may Allah bless him and grant him peace), used to say the following when the month of Rajab began.
اَللّهُمَّ بَارِكْ لَنَا فِى رَجَبَ وَ شَعْبَانَ وَ بَلِّغْنَا رَمَضَان
“Oh Allah! Bless us in Rajab and Sha`ban, and bring us, oh Allah, [...]

بِسْمِ الله اَوَّلَهُ وَاخِرَهُ
In the name of Allah in the beginning and the end.
(Abu Dawood)

بِسْمِ الله وَعَلَى بَرَكَةِ الله
In the name of Allah and upon the blessings of Allah.
(Al-Hisnul Haseen)