Im not sure what you mean by "emotional relationship", but in general, the main messege of Islam was to eliminate all "middle men" , whether "men" or idols. You pray directly to God.
If you mean the relation is based on fear only, this is not Islamic. Rather one should always be between fear and hope, not going to extremes either direction. To love God, and the prophet peace be upon him, are surely Islamic, and is the position of any true believer. The more one loves God, the more it shows in the persons actions/beliefs following the teachings.
However, if what is meant by "personal relationship" is freedom to accept things contrary to what the religion teaches then this isnt to be considered from God anyway, but more like whims and desires.
That said everyone should have a good relationship with God, and raise his/her level in the eyes of God, and become close to him through prayer, adherence to teachings, voluntary prayers, fasting, charity, helping people, and so on.
The Prophet (pbuh) said: "The most loved people to Allah are the most beneficial, the most loved deeds to Allah the Exalted are making a Muslim happy, revealing his sorrow, paying his debt, or revealing his hunger, and I'd prefer to help my Muslim brother who is in need of something than staying in the mosque for praying (I'tikaf) for a month, and who stopped his anger God will cover his private parts, and who absorbed his rage (and if he wants to leave it he would do it), God will fill his heart with satisfaction on the Day of Resurrection, and who walked with his Muslim brother in a need till he attained it God will attain (strengthen) his feet on the day when all the feet will fall (slip), and the bad morals decays the deed as when the vinegar decomposes the honey"[classified as Hasan by Al-Albani]
