For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
In my opinion, there is a connection between prayer and fasting although it was not explicitly mentioned in the scriptures. When we do fasting, the body (flesh) tends to become weak so that you will be transformed into spirit realm from the flesh mode. Unless we merge with the spirit realm, our prayers may not be powerful. This is the reason why we do fasting. There are people who do fasting just because of fasting. That kind of fasting does not have any effect on the prayer.
The way I understand this is that some people are fasting in order to remove earthly concerns from their minds and concentrate their whole attention to God and their prayers. When we eat, especially large meals, additional blood is needed for the digestive processes and not enough is left for the brain. That is why we are so sleepy after Thanksgiving meals. If someone wants to forgo a meal in order to have a clear head and concentrate on an important issue while praying, is fine and Biblical. However, if you have a medical condition (like diabetes) and fasting might harm you, I do not think God would be upset with you for not fasting.
The Bible covers thousands of years of history and only a handful of instances of fasting are recorded which lead me to believe that is not something that God requires constantly from His people. (although I might be wrong)
Hosea 6:6 God is telling us that our sacrifices are meaningless and He would prefer to see mercy and obedience.
Prayer and fasting is prescribed by the Lord Jesus as a instrument to enforce Calvary's victory over Devils. It is not optional: the Lord stated ..when ye fast.... not if you fast. Also in the Old Testament God prescribed fasting to undo the bands of wickedness ,.....,for your health to spring forth..etc see Isa 58:6-12 for more details.