Sebastian wrote on Saturday (read more here) about an incident that happened on Malaysia Airlines flight where passenger in business class had started to go through overhead compartment stealing stuff including cash.
Unfortunately these incidents are not isolated in Asia, although they are most prevalent on overnight flights to/from mainland China. There are gangs that do this as many passengers travel with plenty of cash or other valuables making them easy targets.
When the business class seat next to me is free, I usually strap my bag to the seat using a seat belt.
I once saw flight attendant doing this and it is not usually an issue. Every once in a full moon they may say that it needs to be stored to the overhead compartment for the take off.
The seat next to me is actually quite often empty as long as the flight is not completely sold out in the cabin. It is usually blocked based on the status and can only be unblocked if someone checks in at the airport.
I usually have some electronics inside the bag that I need during the flight. There are also some old passports and few hundred dollars in cash in various currencies.