One balance I've often struggled with in prayer--especially group prayer--is taking everyone's issues seriously but not making prayer some kind of trite grocery list of suggestions to God. What do you do when someone says their dog needs prayer because it's going to get a shot? Or that their grandma got a bad watermelon at the store that she can't take back?
On the side of accommodating, and even encouraging, any and every request are a few things. One, I believe that God is intimately involved in the world and that there isn't anything that escapes his awareness. So on some level, anything that is a concern to someone is a concern to him. Second, I don't believe I have the right to judge the validity of someone else's experiences. So if someone says they are anxious, sad, or angry about something, my reaction shouldn't be to dismiss it as stupid. It may be something that wouldn't matter to me were I in their shoes, but apparently it does matter to them. Third, I believe that God answers prayer. Prayer is not just something God uses to shape us (though it can do that), he has invited us to shape his involvement in the world through prayer.
On the side of not wanting to accomodate seemingly trite prayers are a few other things. One, the Bible doesn't give us many examples of the kinds of prayer. Prayer in Scripture is rich and is far more about the things of the kingdom of God than it is about minor inconveniences or pains. Two, prayer requests like these tend to make group prayer time less meaningful and more routine. It's easy to make a list, check it twice, and talk out loud about it under the pretense of it being prayer. Sometimes it may be prayer, but I know that there are many times I've just prayed for someone's request without passion or desire because I thought I had to. Many times these requests seem to come out because someone really wants to say something, just give an update on their life and not know when else to do it, or spread some gossip. Third, this reinforces that Christianity is all about "me" and God giving me what I deserve. I don't have time to write about all the things that are wrong with that and how that thinking has neutered Christianity.
Something that motivated this is an article I came across by JoHannah Reardon on group prayer. Again, there's no hyperlink button on this computer, but if you're up for cutting and pasting it's at http://www.christianitytoday.com/smallgroups/articles/artofgroupprayer.html.
Your thoughts on the topic?