One must really define what it is they are talking about when asking if prayer changes things. It is certainly the view of the majority that when one asks whether prayer can change things, they are asking if a prayer to a given God can cause change in our world. Typically, the answer to this question will depend on whether you believe in a given God or whether you do not, as shown in the initial posts on this topic.
However, I believe we can answer this question so that both sides of the fence can meet in the middle and, yea-verily, actually agree! Let's just juggle the expectations of the question a bit...
First off, let's be much more literal in interpreting the question. We're asking if THINGS can be changed by prayer. A "thing" is pretty darn wide-open for interpretation. And also, if we're going to be so open minded with our interpretation, there is no mention of God anywhere here, so we can drop the God supposition at this point as well (don't worry, we'll bring that supposition back later, so don't get your knickers in a twist). So now, we're asking if prayer itself, without the intervention of some given God, can change some given "thing."
Okay, now - how shall we define "change?" Heck, we don't have any specific change specified, so it can be anything from suddenly winning the lottery to obtaining personal revelations. Therefore, if we open up our expectations in this way, I think we will find it hard not to say that prayer can change things.
An example: Regardless of your beliefs, someone who prays regularly will become changed in some way. They will possibly become more devout, or perhaps they'll become really pissed off that they didn't win the lottery and in revenge give up on prayer. Furthermore, prayer has done quite a bit toward changing how people feel about donating their money to churches, and thereby more churches are built, which causes changes to the land.
What? Want to be even more literal? Okay - prayer can change the condition of a church since the more people who are there praying, the more wear and tear on the building! Oh, and the knees of a pray-er's pants are just a bit thinner after a really good kneeling-session of prayer.
Now let's add God back in here. If a belief in a God didn't exist, there would be no reason for prayer. Therefore, one has to assume that the pray-er is praying to a prayee (Insert your favorite God here). Whether or not one believes in a God is unimportant - one has to agree that the above examples of change are brought about due to a faith in a God which gave the pray-er a reason to pray in the first place. Therefore, regardless of which side of the fence of religiosity one stands upon, I would think that either side can safely make the logical leap that prayer to God does cause change. So everyone to the fence line and let's all hug!