Depends…like someone said, if the person saying the comment is not with a lecherous face, drooling, and/or staring to one particular place (not my eyes), then I would feel uncomfortable, even if I thanked him. Otherwise, nope. I’ve had both types saying the same comment to me, I appreciated it different.
I once had an older man (maybe mid-50’s) come up to me in a crowded bar in Tokyo and say, “You know what? I’m happily married, but I know a pretty lady when I see one. If I were 20 years younger, I’d buy you a drink.” He wasn’t lecherous, didn’t invade my space at all and wasn’t learning. I think he knew it would make me feel good (all my friends had hooked up with a group of guys and I was the only one not-paired, but that’s because I was engaged at the time).
I find it lovely to get compliments from people, even if they are strangers. Yes, depending on how they do it, it can be creepy. This guy was all class and a really great person to know.
I was flattered. I had a nice little chat with him, and some of his colleagues. Turns out he was very very very high up in the Gateway 2k company. We had a nice chat about a lot of different things and those free $10 Coronas were going down nicely.
‘learning’ should be ‘leering’
Dumb spell checker.
I would think… Gosh, what a sweet man, he must have a kind mom…
I once approached a woman on the Metro and told her, “Listen - this isn’t a come on or anything… but I just wanted to tell you you have a smile that lights up everything around you… so thanks for smiling!”
She seemed very happy that I said that… we chatted for a bit and then I got off at my stop. End of story.
I did it once at a club. I wasn’t trying to pick her up, either. Just walked up and as sweetly as I could put it, I told her how beautiful I thought she was. I couldn’t even believe I was doing it. Her face lit up in a huge smile. She thanked me, hugged me, & told me I made her night.
Not sure why I felt so compelled to do it. She was just gorgeous!
Sometimes them wimmens make us guys do weird stuff!
Wow. I’m surprised at how many women think this would be creepy, and the few that wondered if it meant they had stalkers.
Times’ are a changin’ (Needlessly so?).
My GF gets this kind of thing (More a few years back, but still every once and a while), and when it’s sincere, ‘I just had to say, you’re really beautiful’, she gets a serious charge out of it.
Now, obviously, if it’s weirded out and meant differently, she’ll dismiss it as a creepy guy or simply a loser approach. But when it’s sincere (And she can tell) it really makes her feel good.
I agree with the others - if you say it and you mean it, without strings or the idea that you can parlay it into a date or something, then go for it, what’s the harm. To some women, it can really make their day.
Really, you’re not that different? 
Seriously, though, these aren’t really the sorts of questions I’d feel comfortable asking female acquaintences, and certainly not my SO (well, I knew the answer to the other as how it regards her, and regarding this one, she’s prone to jealousy, so I wouldn’t as her); I figured this would be a good place to ask. It’s just coincidence that I happened to ask them both in close proximity to one another.
Hey, I’ve been here a while - indulge me! 
I would be quite flattered, but very suspisious.
I once had a guy walk up to me at the bus-stop, hand me a flower, and walk away. It was very sweet and put me in a good mood for the rest of the day. But I think if he had tried to talk to me I would have been very wary.
I’d be flattered and smile a big wide smile.
I’d only be suspicious if the bloke (or lass) was hassling me. And then I’d tell them that I’d rather they didn’t bother me any more.
I’ve sometimes said “beautiful!” out loud when passing a very attractive man or woman in the street. I don’t do it very often, though.
“You’re beautiful” is OK; “I just got out of prison today and you’re the most beautiful woman I’ve ever seen” is NOT. (And yes, I have been on the receiving end of the latter.)
I decided to dress up last Saturday night before going out. My ensemble was short of skirt and long on knee high hootch boots. As I was walking down the street to meet my friends, this rasta-looking African American guy with bigass dreds said “Nice boots.” I said thank you as I passed. He wasn’t being agressive, he wasn’t attempting to pick me up, he was just admiring the “boots.” Which was fine. However, if this had come from a frat boy, I might have read it as a more aggressive thing. I don’t know why, but from a laid-back seeming guy, the comment seemed more laid-back.
On the other hand, these two guys followed my friend and I out of the club we were in, stopped us in the street, talked to us, we tried to be polite and simulatiously get away from them, but they followed us down the street. We ended up jay-walking to get away from them.
So I say if you keep it breezy and nice, and make it pretty clear you’re not attempting to get anything out of this girl, then you should be fine. The “have a nice day” ending is classy.
[Hijack] For those of you creeped out or made uncomfortable by such a comment:
Suppose I say it, make no follow-up comment or approach, go away and you don’t see me again.
Would you remember it the next day? Week? Would you feel better about it then? Would you be glad it happened?
[/Hijack]
I’d just smile & walk away. Once I told a guy he has a nice bod. We were standing in line at a cafeteria. He invited me to sit with him, and then we became friends.
If they are respectful, I see no problem.
I get tempted to say it at least a couple dozen times every day, everywhere I go, because I really, really, really hold women’s beauty in high esteem, and to me all women are beautiful. However, I never actually say it.
Today I was in a store talking to the lady who worked there about the merchandise when the whole time my soul was practically shouting and struggling inside me to come out and express appreciation for her beauty; it was all I could do to hold it in. Although she was not the sort this society finds conventionally “beautiful,” the kind photographed for men’s magazines, she was lithe, graceful, and just magnificent, a rare treasure in my esteem. I’m a connoisseur of the often astonishing but too often unappreciated beauty in all kinds of women who don’t match the narrowly defined conventional “beauty.”
That so many of you consider this sincere compliment “creepy” makes me sadder than I can express. It means for sure I’ll never try saying it now. 
Well, this doesn’t really count, as I’m a guy, but I was sitting in the MARTA (i.e., subway) station in Atlanta in about 1990, and a fairly strange-looking woman, one whom I probably never would have looked at twice, went walking by. She looked at me, gave a big smile, said, “Hey gorgeous!” and kept walking.
Now, if she had come over to talk, I would have been freaked out and tried to get out of the situation, but she didn’t; she said it and kept walking. How did I feel about it? Well, twelve years later I still smile when I think of it.
Also I was at a party once and there was a gorgeous girl there. I knew she was a lesbian (a lesbian friend of mine had told me), so I went over to her and said, “Please take this as a compliment and not a come-on: You are the most beautiful woman I’ve seen in ages. Thanks for being here and smiling a lot; you’re making my night.” She smiled and said thanks and I left her alone after that. I’ve never been sorry. (This sounds like Anahita’s story, I know; in fact, I used to live in Tokyo, and when I first read that I thought, “I bet that was my dad!” But he’s never worked for Gateway.)
I did it once. The woman I said it to was all dressed up, and was walking down the street checking herself out in the windows and such. I didn’t get the feeling she was being vain, but rather was just really diggin’ being dressed and made up to the nines.
I said it sincerely and smiled, she laughed and said thanks, and we both went on our way.
There is this girl… she works at one of the local pharmacies.
Holy Cow.
She is one of the most beautiful women it has been my pleasure to see in person. I’m not even sure why, she just is. Makes me feel all squiggly, and want to be dark and mysterious.
She has a light accent (eastern european of some sort) and she just makes me feel froopy.
I have resisted this urge for a few years now, mostly because, see, I have this little picture, that she has been noticing me too…
and I don’t want to fuck it up, soooo…
But the fantasy is there.