I have several #1 fantasies. Hey, why should I limit myself? Often it depends on what she is wearing.

In hot pants, skirt or bikini bottom -- I strangle her with her halter or string bikini top.

If she is wearing a dress or skirt with thigh-high stockings I tie her hands behind her (or to the bed so her arms extend over her head). I slowly strip one stocking off her leg and strangle her with it. I love the look of her dead body with one bare leg and one stocking clad one. Using stockings which need a garter belt, without the belt makes the remaining one slide half way down on it's own. Sometimes I'll be fucking and strangling at the same time! ;)

If she is nude & hog tied I put one leg between her legs and am fucking her as I reach around and untie the string bikini top. It slides up and her tits flop free. Then I slide it around her neck and strangle her while I am fucking her. Tricky, but we actually fucked like this a couple of times. :D Nothing like pulling on the bow and watching the bikini bottom flop open.

stocking tied and knotted around the throat and a wooden stick inserted into the folds of the stocking to strangle her.

I don't have the same stocking fetish as many people here, but a necktie kind of does it for me. Aside from that, a plain soft rope or cord is good, something that won't sever a blood vessel, as Norm mentioned. Don't want the fun to end too soon!

I prefer her bound, in pretty much any location, chair, bed, wherever. Topless isn't necessary but is much, much nicer.

I prefer a sexy woman strangled from behind; maybe she's wearing just a bathrobe or silk-dressing, her feet are bare and she totally ignores what's going to happen. The killer would strangle her from behind, with a thin and cutting wire, until her feet can't touch on the ground anymore. The brutal strangulation continues until she's dead, her dandling feet lost in the air, and her neck marked by a thin purple line. This is what I love: a brutal execution by a cruel and merciless killer, hired to murder the beautiful victim, maybe an unfaithful wife, or politician, lawyer or a precious witness. What do you think about it?

My Sir uses a 3/4 inch leather strap secured in two wooden toggles.

I love to use a silk neck tie and as I am having sex with the woman slowly pull the tie tighter and tighter. Make it almost imperceptible until suddenly she realizes she can't breath.