Over my past 100 or so trips through security at dozens of airports, here's what to know:
1) The new rules allow you to keep the laptop in a sleeve, if the sleeve is form fitting (like the neoprene ones), has no extra pockets, and has no cables/etc in those. I've never seen that challenged since they went into effect. Sometimes you can get by with a more complex sleeve, but that's an exception.
2) The laptop must be by itself in a tray. Sometimes you can sneak in a phone or ipod, but often not. Suggest not trying.
3) I turn mine off (not just suspend). X-rays can do strange things to RAM on rare occasions.
4) I have had to turn it on when going through customs. It depends on the country and if you get tapped for deeper screening. I have never had to turn it on at a US airport.
And just a general tip, allow longer than you remember to get through security. Best resource is
www.tsa.gov.