When I'm passing other riders who are reasonably far right, I use "passing on your left" (spoken as loudly and clearly enunciated as possible) to mean "stay where you are and I'll go by you."

When passing riders two widely abreast, who look unstable on their bikes, or who are individually farther left than necessary, I mean "please move to the right a bit so I can get by you." If they don't move, I'll wait behind them until it's safe and clear to pass.

When passing kids, old people, or families on multi-use trails, I usually say "Coming up behind you" from a good distance away; I definitely don't assume they know what "on your left" means (especially little kids). That gives them time to figure out what's going on and react in a way I can predict and accommodate. I also always say "Thank you," whether or not I could perceive any reaction to my calling out, because I want people to remember me as that polite cyclist who slowed down to pass, rather than that jerk who blew by at 20 mph when passing a 4-year-old on training wheels. No need to foster more cyclist-non-cyclist dissension than there already is.

I do NOT expect people to move to the right for me, unless they're unreasonably far left. When people say "On your left" to me, I generally hold my line and speed since I put myself as far right as is safe in any given situation.

Slight thread hijack: On the STP this year and last year, we were passed by hundreds of people who didn't say a word when they went by. They silently passed us, often in groups of 10 or more, and that really bugs me. After a while we started calling "Bikes back!" to the other riders in our group to warn of these stealth passers. Is it reasonable to feel irritated when people rudely pass without saying a darn thing? Is there any law that says you need to notify somebody before passing? (I doubt it; I think this is probably just common courtesy.) Especially in big group rides when you're almost always being passed and almost always passing, it seems like saying SOMETHING should be the norm for everybody.