Pets bugging people for food is not usually a pet problem, but a people problem. By giving them food, you are reinforcing the behaviour that it is OK for them to ask for it. The more you do it, the more pesky they will become.
What I learned through various sources, including Cesar Milan's "Be the Pack Leader" is that in animals, in Milan's case dogs, but I've found it applies to cats as well, the dominant members eat first. You can see this in a pride of lions, when the lionesses do the hunting, but wait for the lions to eat first, and then the cubs eat after the lionesses.
What I do in my home, is not feed the animals until I've eaten. While I'm eating, I don't acknowledge them at all, and I will reprimand them with a gentle
push or a snap of my fingers if they try to interact with me. If I have some scraps, leftovers, or treats that I want to give them, I keep it aside and give it to them, in their food bowls, when I am done eating.
They have learned to not disturb me, or my guests, when we're eating. This makes for an overall more enjoyable experience around them, rather than being embarrassed and fight with them.