Self Check in.
LH - I used this at MUC but for internal flights only. They were planning to expand it (this was 1999).
BA - I have used this internal in the UK and long haul at T4 and, with the fast bag drop there it was fine. I was going to use it coming back from the US in March but I was on the early morning flight and the machines, "... are switched on by London and they don't do that till later." I queued and was seen in a reasonable time. When I left the counter, I checked the machines again and they were now on - this was about 07:00.
The problem will be that a goodly number of people do not know what actions to take at the auto machine. I suggest that the machines are easy to use and pretty much idiot proof but they LIKE the fact that they arrive at the counter and just abandon any sense of responsibility! They LIKE having someone to shout at.
I agree that auto check in has to be the way to go and will steadily increase as computer savvy passengers increase. In other words, as the old ones stop travelling!