I have a number of hubs on this exact matter. If you'd care to jump over to my profile & check them out :)
In short ~ yes, it does exist. It is very real.
If I had to pick a single example out of the millions in my life...hmmmm... let me think:
I wanted to be a stay at home mom & hubby wanted me to go get a job, when I started looking my van broke & I was unable to do what he wanted, so I was literally forced to stay home like I wanted.
I wanted to show the birds to my toddler out the window. They were all pretty far away in the yard. I wanted him to have a closer look, but how? Wild birds don't tend to fly too close to people. In less than a minute a chickadee came flying right up to the window. Super close & my toddler got a fantastic view of it.
I wanted to earn money from writing. Mainly I have a book I'm working on in the editing phase. I wanted my income to come from a way for me to still stay home. I had forgotten all about HP, until I really started longing for an income to come from writing. Wham, I remembered about HP and in less than a couple of months of being back I'll be getting my first payout soon & my traffic and income keep increasing. So, not only will I be getting paid from here, I'll also be getting an at home income when my book is finished.
Alright, it was more than a single example... I'm kinda wordy, which is why writing is so perfect for me :)