I had my bike stolen once by an airline. I was flying from the USA to Germany and I never saw my bike again after I gave it to the airline. It was, unfortunately, at the beginning of my trip. My bike was packed in a box along with a few other items including my sleeping bag and handlebar bag. My intention had been to bike to a small town in SW Germany where friends lived, and then my friends & I were planning on biking and camping together mainly in France. There happened to have been 3 other passengers with boxed bicycles on my flight, and their bikes all arrived. There were several other passengers, however, who each had a piece of checked luggage stolen. (we all filed our claims together in Frankfurt) I'll never know for sure where my bike was stolen, but I have been told that Frankfurt airport had a serious problem with stolen luggage at that time. It could also have been stolen in the US airport, of course.
What did I do? I took a train to my friends' town. I thought I wasn't likely to ever see my bike again. One of my friends had an old bike which I borrowed for our trip. It worked out fine even though the frame was far too large for me. We didn't camp since I had no sleeping bag. We biked across the Massif Central, the Dordogne region, and the Pyrenees over the next month. Despite having lost my own bike, it was one of the best trips I ever took.
There was an almost unbelievable postscript. At the end of the trip, the SNCF (French railroad) managed to lose the bike I had borrowed from my friend. They found it 3 days later. I couldn't believe I had lost 2 bikes on 1 trip, and after 3 days in Strasbourg, I was going to leave whether or not my friend's bike showed up. It reappeared, and I quickly biked down the Rhine valley to Frankfurt, then shipped my friend's bike back to his hometown on the Deutsche Bahn (German railroad).
2 years ago I had a small shortwave radio stolen from my panniers in Spain. I haven't had a problem with theft during my trips in developing countries.