It depends on the airport and the airline.

Generally they just check your baggage, letting you avoid the long lines at ticket counters and proceed directly to the gate to get your boarding pass there. They can be a big time saver. As for the risk of baggage being stolen, I would think it would be minimal. When flying on an E-ticket, I like curbside checkin for my bags and the E-ticket machines for boarding pass. Very quick process.