Interrupting the food talk to say -
I miss a day or two and there's been a whole great discussion of prayer! I'm chiming in belatedly with some thoughts that reflect my personal beliefs and understanding within traditional Judaism. No disrespect to any other tradition, beliefs, or lack thereof is intended.
In Hebrew, the verb to pray is reflexive - l'hitpalel - (similar to the verbs for to wash oneself, to dress oneself, to communicate with another or to correspond with someone by letter). Traditional Jewish prayer is a mix of mostly set prayer as well as spontaneous prayer, based around acknowledging G-d, thanking Him, praising Him, and making requests of Him.
I heard a lecture once that explained that 1) if G-d is all-powerful, then He can give you whatever you ask for, 2) therefore you should ask and expect to receive it ("I want $1 million today!"), 3) if you don't receive it, ask why, 4) check whether you're asking for what you really want and whether you're ready to get it.
For eg., the person who wants a million dollars may really want to get out of debt, and needs to look at ways to change his own behavior so that he could be a good steward of money. Someone who prays to become captain of the basketball team may really be asking for the self-confidence to be a leader. Understanding what you're really asking for, or should be asking for to grow as a person, is a way that prayer changes the pray-er, which is one way G-d answers prayers.
I do not pretend to understand what this means for people praying through impossibly painful or difficult situations. I believe that not understanding everything is part of the human condition and that G-d, Who does understand everything, really does love us and know best, even when we can't see it in His actions.
Hebrew also has the word "kavvanah" - intention - and that's what distinguishes a rote recital of words from true prayer. Without kavannah, prayer is rather insulting to G-d - would you hold a conversation with someone you loved and give them that little of your attention? It's all about the relationship - the direct, personal, constant, two-way relationship between G-d and man.
Happy first-night-of-Chanukah to all for whom it is meaningful. (I'll say Merry Christmas when appropriate, too.)
With apologies for being both long-winded and late to the conversation.