Flying recently with BA I've found online check in quick, straightforward and simple. I have had one problem, and that was due to a glitch caused by a change of booking.
Never used KLM, but their website isn't really compatible with anything other that IE - which possibly highlights problems in their systems!
I disagree with IB4138 - I have printed boarding cards off on rubbish paper on a rather poor quality inkjet and been read at security no problem!
As for OLCI being useless in the States I don't totally agree - last time I flew back from the States, everyone else was checking in at the airport. So I had a completely clear queue for bag drop! The queue for check in was out the door. And this was not long before check in was due to close...
And finally from me - whether you check in online or not, there is always the possibility for an upgrade! And no, I don't mean if you put your hand in your pocket. I've been upgraded twice at bag drop
