I never asked for anything...
In one case, a thunderstorm made me and just about everyone else connecting at CVG miss our flights to Europe. I was Gold Medallion at the time.
They rebooked everyone (hundreds of us) on flights the next day. They got me a hotel room, some vouchers for food, a phone card, a shuttle to the hotel, and an amenity kit (like the ones in Business Elite, with a toothbrush, etc.). I didn't realize until later that the hotel was "all expenses paid" -- no minibar, phone, etc., charges. And I got my upgrade on the non-stop flight to Europe the next day (a lot of the others had to connect, but they seem to get the Medallions the best flights).
Another time (this year) a late AF flight caused me to miss my AF codeshare in Paris (going to SFO). AF paid for a hotel & food (3 meals, nice meals at that -- it was France!). And they got me a paid business class seat the next day, since there were no upgrade seats available.
For delayed luggage, an amenity kit is about it. This only happened to me going home, so no big deal. And they delivered the luggage to my house.
I did get a voucher for a delayed flight (that I boarded minutes before takeoff, so it wasn't I who was delayed).
In all cases, I thought the resolutions were fairly generous. I have no interest in trying to extort anything more from the airline -- they are not just a pinata of goodies waiting to be burst...