There is, fundamentally, a problem in attempting to analyse results as evidence of intercession: correlation is not the same as causality; stating that "we prayed for him, and he recovered" is not the same as demonstrating "we prayed for him and this is what caused him to recover". He could have recovered through any number of routes:
- natural body recovery
- medical help (I've heard that can help)
Ultimately, there is no "control group" in an individual scenario such as this to provide any meaningful way of interpreting the result. Additionally, a single event has absolutely no statistical relevance; at the individual level, all bets are off. As Rex Kerr has already noted, attempts to scientifically study this (with proper control groups, etc) have not gone so well.
Another issue here is the human mind's ability to celebrate success and forget failure (similar to the way in which a gambler forgets all the many times he has lost, and uses the fewer number of wins to justify their habit):
- when the desire of the prayer works, it is often shouted from the rooftops, used in headlines as evidential proof, etc
- when it doesn't, people are reasonably sad (quite often it means somebody has died), but it is not given the same announcement; I really can't envisage a headline "Alleluia! Our prayers for Tony's illness have been answered! God has spoken! He died." (please forgive the morbid tone)
My point in the above is not to say "prayer is useless", but rather: the anecdotal evidence is itself naturally biased towards to positive; since the negative is dismissed.
In my view; if you feel that prayer helps, pray. A good friend of mine had these sage words to say on the effectiveness of prayer:
In my view, God's already with this newly growing family, and is looking after them and loving them. That's what God does. I waver greatly in terms of what prayer does, what it can accomplish etc, but I think I'm generally of the opinion that it's more to influence our actions than God's. If praying makes me more aware of their needs, even just by giving me space to consciously think of what they might be going through and how I could help, how is that a bad thing?
These are not my words, so please don't interpret "more ... than God's" as me saying prayer doesn't work - but if prayer causes the praying person (the pray-er?) to act more towards the goal, then in that sense it might demonstratively work (to the non-theist: reflection may achieve a similar aim).