Once BA misconnected a bag of mine between longhauls and between LGW and LHR. After filling in the PIR, they were going to let me go. Just in time, I remembered to ask for a cash allowance to buy necessities and got handed some cash - HKD 300, I think. Obviously, the lesson I learned was that you have to ask or you won't get.
As it happened the bag arrived on the next flight (less than 24 hours later).
The other misconnect was again at LHR, from BA to IB. I didn't think I was going to get anything out of the IB staff, so I left it. The bag was about 18 hours late. I wrote a suggestion letter to BA based on the tags that were and weren't on the bag, about how they might make an improvement. They responded with an unexpected voucher for GBP 50 (I think).
The other good BA compensation-for-baggage experience I have had was when they broke one handle on an old and already-worn suitcase, making it very difficult to lift it onto its wheels. After some other airlines had done some more minor damage to it over the following few months, I replaced it with a new and much more expensive case. I wrote an entirely honest letter showing that I'd bought the new case but pointing out that the damage I was claiming for was only part of the overall damage to the old and much cheaper case, and asking only for a small contribution. I got a cheque (not voucher) back for rather more than the old case had originally cost. Needless to say it didn't take long for BA to get that money back.