The worst reaction I have ever received was a polite, "Thank you," this without a smile, then a quickly turned back. That was the worst and was very unusual.
Generally the reaction is very positive. It takes a very stuck up individual to not appreciate being told that they are special, or exceptionally attractive. Much of course depends upon how you give your compliment.
If you dress like a slob and approach the woman with a drooling grin on your face, staring at her breasts, don't expect a good reaction. If however you act as a perfect gentleman and are articulate in your delivery of the compliment, you will make her day.
It is best to not advance toward the woman you wish to compliment directly. If she sees you barreling towards her, intently focused upon her as a target, she will understandably be feeling defensive and maybe even a bit worried. Most women have way too much experience with boorish creeps who have no manners and less respect. Approach her quietly in a totally natural fashion such that when you speak to her, it is a bit of a surprise.
What you say and how you say it is of pivotal importance. So important is it that you might want to formulate your compliment before hand and rehearse it a few times under your breath before you approach her. You will probably be feeling nervous and not knowing what you are going to say when you open your mouth is likely to result in you standing there with your mouth open, stuttering. This does not make for the best impression.
First of all act like a perfect gentleman. You are standing in the company of the Queen of England, act like it! Your eyes should look into her eyes (preferably) or at the floor, do NOT stare at her body. If it is her attire that you are complimenting, you may for just an instant AFTER you have paid her the compliment let your gaze sweep over her clothes.
Be formal, you have not been given permission to be less. Address her as "M'lady" or "Mizz". For a woman of advanced years (over 60) you may use the word "Madam". Do not use the words "Mrs." or "Miss", as some women may take offense at an accidental misuse of the term.
Exactly what you say is a rather individual thing and depends of course on whom you wish to compliment. Whatever you do, do not lie to her. Find that thing about her that is most noteworthy and congratulate her upon it. Try to be articulate, even poetic in the words you use. Let your words convey the awe that you hold her in.
Once you have paid her your compliment, give her a short polite bow, a nice smile, then take a step backwards. She will always say something in response. Accept what she says with a smile then leave. Yes leave. Any person loves to be complimented but few of us are used to it. She will likely be extremely flattered but at the same time will be feeling awkward. To not force her to deal with that awkwardness. By leaving now you make your compliment a perfectly positive experience.
Realize that the fact that you have paid her a compliment does not give you license to invade her space or to be anything more than a polite stranger. The effect of a compliment will be that the next time you meet she will likely remember you and be much more receptive when you simply walk up to her and say hello.