Not really sure if this qualifies as using miles for others since I used them for myself on this trip, but here's my input. Also not sure how it is specific to AA, but I'll leave that up to the mods to decide.
I booked a last minute surprise trip to Dublin in March for me and my (then) girlfriend. She always wanted to visit Ireland but has never had the finances or opportunity to do so. Since I was unable to sneak her passport without her knowing, I told her the morning of our departure that we were going to Toronto and to bring her passport. I know, Toronto in March doesn't sound like the ideal getaway but I had to get her to pack for cold weather and she was excited nonetheless. I had to come up with things we were going to see and do while there on the way to the airport. When we arrived at the ticket counter to check in the TA asked "Any bags to Dublin today?" The look of utter shock and surprise was priceless (and I was beaming too). The real purpose of the trip was to propose, which I did at the Howth hills east of Dublin (she said yes). That area is absolutely beautiful and Connolly's pub is a fantastic place to grab a pint of Guinness and some lunch after walking the trails up the hill.
To add to the surprise, I snagged 2 seats in BA F (on the 77W!) for the LHR-ORD return leg. This is the best way I've been able to put my miles to use for others so far. Hopefully one day I'll have enough to spend on friends/family that want to go somewhere.
Great idea for a thread!