Does God "hear" eveyone's prayers?

Does God only respond to the prayers of Christians or does He also respond to the prayers of those of other religions?

Obviously God "hears" the prayers of everyone since He is omniscient. But Jesus seems to imply that Christians have a special hearing in the presence of the Judge. Jesus says, "Whatever you ask in my name, this I will do, that the Father may be glorified in the son." (John 14:13)

Moreover, since the wrath of God abides upon those who have not believed in the Son (John 3:36); it follows that they should not expect answers to prayer from the Father.

Obviously God does answer the prayers of the unbelieving. But He does so out of His mercy and divine plan for humanity rather than out of a sort of obligation to the followers of the Son (John 15:7).