Or lack of one, as the case may be; my thoughts echo Dannys in that respect. Yes, there's a Divine Plan, in which each of us has an important predestined role; that said, there's also free will, which allows each of us to opt out of the role created for us (and for which we were created). Ideally, we have a cooperative relationship with God, where we work in concert with (but always subordinate to) Him toward mutually desired goals. To that extent prayer is very important and can take many forms; prayers for things that directly conflict with the Divine Plan will not be granted, but things in accordance with the Divine Plan and directly beneficial to an individual personally won't simply be dropped in his lap: He'll usually have to work AND pray for them. Darth Katie mentioned the parable of the unrighteous judge, which I tend to think of in terms of ranagrandes answer: The difference between a prayer for a momentary whim and a strong desire or even need is often the difference between asking God for something once and asking Him for it several times a day for years.

The bottom line, IMHO, is that several things are necessary for a prayer request to be granted:

1) You have to pray for it (obviously), usually for an extended period.

2) It has to be in accordance with and submission to Gods will.

3) It has to be made with faith, both that God will hear and answer the prayer, and His ability and will to do so in the way best for you.

4) It usually has to be in the context of a larger general cooperation and submission to God.

In the last case, that's not to say God won't take pity on an unrepentant sinner lost at sea, but when He does it seems more an act of pure compassion than an answered prayer for rescue. Maybe I'm taking David a bit too literally, and maybe he got some mental scars from the episode with Bathsheba, but one point to which he returns repeatedly in the Psalms is that the prayer of an unrighteous man is basically pausing while spitting on God to ask Him a favor, and gets the kind of response you'd expect. Selfish prayers and/or those only made when someone wants something come very close to that, too. Again, prayer is by nature part of a cooperative relationship with God, and the quality of the one is directly linked to the quality of the other. Consequently, in much the way Vivien suggested, when ones relationship with God is strong He often grants prayers by providing the means to achieve ones requests (which, ultimately, He does with all "our" achievements whether we realize it or not, and part of a healthy relationship with God is gratefully acknowledging that in prayer. )