Jai Sai Ram. Compared to you all, I'm still a fledgling devotee and I haven't had his darshan yet (maybe I should say my time is not ripe yet). But I can share some of the experiences that my parents had and how I turned towards him. This is not just one experience that I'd like to share. It’s a gist of multiple leelas (selected among many).
I'm from Andhra Pradesh born to a Telugu Brahmin parents in the coastal city of Kakinada. Both parents were state government employees. They are totally god fearing and never were corrupt in any of their dealings. Accordingly as the normal practice goes, they were always transferred to places where most of the other people don't wish to go. My parents never flinched from these transfers. Today they both are retired and in the waning years of their life but still helping others as much as they can.

How I turned towards Sai:
During one of these transfers for my parents, in 1991 I got a chance to go hostel and study at one of the residential colleges in Andhra Pradesh. There we had a small temple next to our hostel and we all used to go there and offer our prayers. There, the priest once told me that I should say the name Sai Ram whenever I get a chance. This was the first time I can recollect I had turned towards Sai. But I was never aware of any parayanam books or never interacted with any Sai devotees at that time. I don't think I'm even aware of his leelas at that time. I was still carrying over the values imbibed in me by my parents. So I used to recite Aditya Hrudayam and Vishnu Sahasranamam without fail. Later on at one point, I did have some very bad experiences in my life (1998 to 2004). That time I really revolted against god and stopped praying to him. Later with his grace my faith towards god got restored in 2004 ending. When I reached US in 2007, I had a roommate for a short while who is an ardent devotee of Sri Shirdi Sai. It was he who brought back my life back towards his holiness Sai.
During all these years when I had my ups and downs in life my parents were unflinching in their devotion towards Sai. My dad for me is unfathomable but I can for sure say that my mother is all praises for Sri Shirdi Sai. I'll narrate two leelas that my mother had seen happening and one from my side.

Leela 1:

My father the most uncorrupted person, all of a sudden has received a dream transfer order to a very lucrative place also with a promotion as a Divisional Engineer in APSEB. This is quite uncommon for a simple person like my father. Only the politically and financially well connected people can get easy postings here. It's Vijayawada Thermal Power Station, Kondapalli. There my father has started his tenure as a Divisional Engineer and was doing his duties without fail. Based upon seniority my father should have become a Superintending Engineer quite some time ago. But we saw many people equally qualified (BE/BTech) but much younger in age becoming an SE and above him. My dad always brushed aside my words like this: “It's not for me; I don't even want to think about this. I'm sure it won’t even come to me”. But first divine intervention came in the form of a non gazzeted employee who was fond of my father. I'm sorry that I cannot recollect this person's name. But about 1 year before my father's retirement he started pestering my mother that my father does stand a chance of becoming an SE. He only has to be vocal and file for his promotion. But my father was unmoved. He simply rejected his words and never even tried it.

But my mother didn't give up. Just a few weeks/may be a week before his retirement, she started Sri Shirdi Sai Parayanam and finished it by offering kheer as a prasadam. After placing kheer container infront of him and while she was putting in a pinch of sugar the bell sounded. We used to stay in the DE quarters in the first floor. So when the bell rings, the person in the first floor should come into the balcony and check who has sounded the bell. So my mother went out to check who it was. I'll state what happened then in my mother's words:
"There was a tall guy wearing dress exactly like Sri Shiridi Sai standing near the door that leads to the first floor steps. He told me that he is coming from Shiridi and is distributing prasadam and udi to all the people. After I had taken the prasadam from him and climbed up the stairs, I don't recollect seeing him again. But the moment I reached the living room from the balcony the phone allocated by the office rang. It was the same non gazzeted employee calling from the office. His voice was bubbling with happiness. He said amma saar ki SE gaa promotion vachindi--- means Mother, sir is promoted to SE."

That incidentally was the last day of my father's service with the state government and by the time this call was received by my mother, my dad has already taken the retirement and he has signed the papers. All of a sudden with his grace, time started moving backwards. With appropriate very legal moves, the people in very high levels of the APSEB have asked my dad to go to Kothagudem thermal power plant and take charge as an SE. He held this post only for 1 day (on the day of retirement and the next day to take charge and then retire as an SE the next day). Materialist people may think "He was an ek din ka sultan" but he got it when there was no hope of getting anything close by. When this leela has happened, I'm not that lucky and I was away from home. My mother mentioned this to me.
 

Leela 2:

My mother has an elder sister who remained a spinster throughout her life and she worked as a government teacher in Chennai, Tamilnadu. When she has retired, my mother asked her to come and stay with us. My father being very simple he never denied my mother of any of these doings. So she came from Tamil Nadu and her pension got stuck up in the bureaucracy there. With his grace, we are not poor and hungry. But this not getting of pension was causing my maternal aunt more tensions. So my mother decided to do the parayanam once more but this time along with her sister. As usual after offering the kheer, the phone call came from her now ex-colleague in that school that the pension is sanctioned and the check is already deposited. Don't we call this a leela?

There are many more incidents but one thing I'd like to share (my most recent experience with Sai).

Leela 3:

The maternal aunt in leela 2 as I mentioned is a spinster and was staying with my parents. After my parents vacated the government quarters in VTPS, Kondapalli and KTPS all three of them moved back to our home in Kakinada, AP. Starting in 2010 she started suffering a lot due to diabetes and heart enlargement etc. She became extremely weak. My mother or servant maids had to take care of her. Once during one phone call that I made from USA, she mentioned to me over the phone like this. "For the first time another person has given me a bath. Looks like time is nearing". Just a few days after saying this, on 10 July 2012 she was sitting in the living room watching an old classical telugu movie on the TV. My mother walked into the living room and asked her if she would like to relieve herself. She consented and while walking from the living room to the bedroom where there is an attached bathroom, all of a sudden she said with an enormous amount of clarity "dear brother in law please hold my shoulder, I think I'm unable to walk". That was for the first time she ever permitted any man of her age group to ever touch her. My father rushed towards her side and held her hand near the bicep region and she said "I'm feeling sleepy, let me lie down" and she lost complete control and collapsed on the bed. My father it seems had seen the life going out of her eyes. Then he held her feet and adjusted her on the bed and slowly the news started trickling out. She stayed with my parents for more than a decade she passed away on peacefully on July 10 2012 literally in my parents hands. Now I'm in USA stuck up with visa problems and unable to travel to India. It was still wee hours for me on July 10 2010 and when I received the call from my father at that hour, immediately I had a bad feeling. They were confirmed by my father's words. I always maintained that tough guy's posture for my family and I had a tight feeling gripping my heart. When the phone call arrived, I was sleeping on the floor with my laptop still running next to me. I immediately typed sri Shirdi Sai into the google and you won't believe what I saw. This is the leela that I had seen after hearing the bad news. The text that appeared on the screen was "Don't feel sad for the people who have passed away. Always understand that they are safe with me and I'll take care of them". There are many quotes by Sai. I would have seen "Shraddha and saburi" or "feed the hungry". But this quote explicitly appearing before my eyes when I received this news is really a leela for me. In the following days when I heard through relatives over the phone that my mother was secretly crying the bathrooms I called her and told her of this experience. She at first was surprised and kept on asking me if I had really seen this text on my laptop. When I did answer in the affirmative, she is slowly absorbing the reality and also finding solace that my aunt is now in Sai's protection.
 

The biggest leela that I'd like to mention is:

For quite some time I have been thinking of sharing some of my family experiences but never did share them. But all of a sudden I see an email for Sai trust asking us to share our leelas. And I immediately typing all these leelas and sending them to you. Don't you all call it another leela?

Peace be onto all of you.
Jai Sai Ram.