Mozart will meow sometimes, but he has an almost silent one, so I think it's just adorable. He stops when I tell him 'not now'. If I'm at the front door, Ginza will ask sometimes, or get up on his hind legs and wrap his front ones around my waist, or if I bend down, wrap his paws around my neck asking to be taken outside.
After some experimenting, what works for our household is if the outings are at random times on random days. Then they think it's a treat, and they don't expect it, so they're not demanding it. I'm also extremely consistent about the procedures, which is why the kitties expect me to lift them up and carry them out, and never think about dashing out the door.