In my case, the most memorable answer to prayer was the miraculous healing of my wife's father who suffered an aortic aneurysm. We were told he had just one or two hours to live and his organs were failing by the medical staff when we arrived at the hospital. My wife and I had been praying several decades of the rosary on our way to the hospital. At his bedside, my wife handed me a small Gideon bible and asked me to pick a reading. I randomly opened a page and read these words from psalm 91:
Because he loves me, I will give him long life
I passed it back to my wife and showed her the reading, and we looked at her father deeply unconscious on a morphine drip. A few moments later, he started to cough, the nurse removed his oxygen mask, he opened his eyes and said, "clear off!".
We were ushered out of the room while medical staff were called in. He made a miraculous recovery (in the words of the ward sister) and lived several more years before God called him to heaven, and he was able to look after his wife who suffered from severe arthritis.
So not only did the unexplained event coincide with the prayers, it was confirmed by a scripture reading just before it happened. No doubt you will write it all off as coincidence, but how many coincidences does it take to make a miracle?
But this is mere anecdote - you have no way of knowing whether your father-in-law would have made a recovery had you not prayed, as there is no control.
And of course, there are countless other examples, where people have prayed and prayed for recovery and the person prayed for still died - perhaps when he finally died you were praying for him at that time too.
The only way you can draw any kind of meaningful conclusions is through proper controlled research and there have been a few such studies. You also need to factor out the placebo/nocebo effects where a person may feel better or worse through the psychological effects of knowing they are having an intervention (whether medicinal or prayer) which has nothing to do with any potential direct impact of the intervention.
So the best example of research of this type looked at complications and recovery rates for patients following heart surgery. There were three groups:
A: Where a group of people actively prayed for recovery and the patient was aware they were being prayed for.
B: Where a group of people actively prayed for recovery and the patient was not aware they were being prayed for.
C: Where there has no prayer intervention.
The results showed no difference between groups B and C - on other words prayed had no effect on recovery other than through a psychological effect if the person knows they are being prayed for. Interestingly group A had the worst outcomes - so while prayer had no actual effect knowing that people are praying for you actually led to worse recovery, presumably because the patient concludes that their condition is worse than it actually is if people are actively praying.
But hey, ho, let's not let some real evidence get in the way of anecdote and blind faith.