I go weak for tall, but not too tall. I am 5’7", so 6’1" would be great.
Height is not the only factor, of course!
I know my sister has a horrible innate bias against short men. She dislikes her daughter’s boyfriend, an otherwise decent guy, 'cause he’s short.
6’ tall here.
Former husband is 5’6" and has no trace of Short Man Syndrome whatsoever.
Currently seeing…um. 5’8", 5’11", 6’0", and 6’4" (yep, I’m poly) and like them ALL.
I do have a certain preference-- that the guy not be exactly my height, as it makes one of us putting our arm around the other’s shoulders a bit awkward. EITHER taller OR shorter works just fine for that. But I don’t mind holding hands, either (which works fine at the same height).
I do notice that while most women seem to catch on to Short Man Syndrome pretty fast, there’s a lesser known “Tall Man Syndrome” which consists of, apparently, wanting to be given a cookie merely for the length of your inseam. Sure, being tall(er than your date) might be a “plus” in many women’s books, but if you don’t add something else along with it, you’re still a zero.
Corr
I like tall guys. I’m 5’8" myself and seem to have trained myself to notice taller guys more easily than shorter ones. When it comes to actually dating, though, I find the best range is about 5’10" to 6’2"–tall enough to be noticeably taller than I (which gives those “protective” vibes) and just about the right height for embracing standing up or walking holding hands.
I am generally attracted to tall men. Tall and muscular, with broad shoulders, but not gym-apes with huge upper bodies and tiny legs. It’s nothing intellectual, it seems to be how my attracto-meter is wired.
Both my serious relationships have been with men who are 6’4". I’m 5’5", and the only difficulties are kissing while standing up and dancing. But there are plenty of other ways to kiss, and my husband doesn’t like to dance anyway.
I don’t have anything against shorter men, I just don’t find them sexually attractive as a rule.
I’m a titch under 5’11" (and female), so Short Man Syndrome can be real problem for me. I don’t give a whoop in hell about how tall men are but most of 'em–IME–care a lot. The absolute greatest guy I ever dated seriously was 4" shorter. My being tall didn’t bother him a bit, so everything was completely cool.
If my height doesn’t bother the guy then his height, no matter what it is, doesn’t bother me.
Besides, there aren’t all that many guys taller than I am.
Sigh.
What about those of us as tall as you? Do we still get a shot or should I stop hoping? 
I’ve always dated guys who are taller than me, which is not very meaningful seeing how I’m just barely five feet. No real preference (then again, I tend to put much more weight on personality than looks, really).
The preferable range for me is between 5’7" and 6’1"-ish. I like for a guy to be a couple inches taller than me (I’m 5’5") and around 6’0" it gets awkward to kiss standing up–my BF is 6’1" and I have to stand on tiptoe.
That being said, if I really wanted to date someone, I wouldn’t let height stand in the way, unless he was significantly shorter than me.
Let me rephrase that. I’m less likely to be attracted to someone who’s significantly shorter than me. If I was already attracted, it wouldn’t stand in the way of dating.
Hey, I like a man I can see eye-to-eye with. 
I’m 5’5" so I’ve never gone out with a guy who was shorter than myself. Personality and other aspects of physical appearance are what I notice. I’d probably find it awkward to have a boyfriend who was taller than about 6’5’, though!
I’d be happiest with a man who is shorter than me, but since I’m a mere 5’3" that’s never going to happen. Still, I’m most attracted to short men. It’s incredibly unromantic to get a crick in one’s neck while trying to get a glimpse of a face. Plus, I have a rather cough dominating personality, which makes physical inequality frustrating. You girls can keep your tall men.
You never know. I know a real hottie who’s 5’2" or so. Maybe 5’2 1/2".
Corr
This can be a bit of a sore spot for me. I’m 5’10", maybe 5’11" depending on who’s measuring (scoliosis can do interesting things with your apparent height). In college I dated men who were shorter, taller, and about the same height. The difference was primarily in other people’s attitudes toward us as a couple and, in one case, the attitude of the man himself. People, even people I knew who otherwise didn’t seem like the judging sort, didn’t think it was “right” somehow for me to date a boy who was noticeably shorter than me. And the guy who was (if I remember correctly) the shortest guy I ever dated had a major, major attitude problem about it. Not just the “I don’t like it when you wear heels” problem, but the “I will go into a major sulk if anyone mentions our height difference in any way in my hearing” problem. Looking back, this should have been a warning, as he really was a jerk in many other ways as well…
At the same time, I knew two girls who were on the short side, 5’2" or so. Both bragged that they would never consider dating a man under six foot tall. And people thought this was “cute”. My feeling was that if society insisted that women could only date men taller than themselves, thereby greatly reducing the pool of available men for us tall women, the least they could do was to declare that small pool off-limits to short women!
Of course, that was college. Now, I’m married to a man who is… hmm… I’d guess about four inches taller than me. And he’s the shorty in his family. Our 11-year-old son is already up to my upper lip, I suspect both our kids are going to tower over me, and possibly their dad, when they are grown.
Getting back to the original question, though, I don’t find height in itself attractive, no. I do find being comfortable with one’s own body attractive, so a tall man who walks tall is attractive in that way, and so is a short man who doesn’t need to “compensate” for his lack of altitude by developing an attitude.
Since I stand 6’4", I’ve been lurking in this thread out of curiosity. I just wanted to say that this is one of the best, most colorful phrases I’ve heard to describe the so-called Napoleon complex. Well done! 
I can find men of all heights attractive, and have casually dated at least two guys shorter than me. However, of my three “serious” exes, one was 6’2", one was 6’3", and one was 6’6". The perfect man wrapped up in a 5’6" body probably wouldn’t get tossed to the curb, but I have to be honest that I do prefer a guy with height. One of the things that makes me first notice a guy is if he looks big enough to make me feel small. (I’m 5’5")
Personality is the final influencer though, so a shorter man has just as much likelihood of being a good match but he might have to work a bit harder to get noticed. Which is probably about as comforting to all the short guys reading this as those “women don’t have to be super-skinny, just…” is to all the chubby girls when those types of threads roll through. People are odd.
Height, or lack thereof, has never been an issue for me. I’m about 5’9’’. My husband is 6’3’’; however, I’ve dated guys that were my height or shorter (shorter meaning around 5’6’’) and never thought a thing about it. As flodnak so eloquently put it, as long as the guy doesn’t have a problem with it, I don’t, either.
Count me in with the “it ain’t the height, it’s the compensation” crowd. I realize it’s just my own personal experience and not universal to all short men everywhere, but every one I’ve ever dated has been compensating and therefore aggravating to be around because of it. As I’m fairly tall for a member of the distaff set (5’9), I’ve dated a few guys shorter than me - and it didn’t disturb me that they were shorter than me (although, to be truthful, I don’t like them to be littler than me - I hate feeling huge as well 
), but it always seemed to bother them.
Partially as a result of that, my fiance is 6’4 and a bit.
I personally prefer guys with height. My last boyfriend was about 6’2-3, and I am about 5’4 without shoes. But I have lots and lots of fantastic heels to help out too. I have always been attracted to guys that are taller than me, significantly taller usually. I think it’s just a specific body type that I like, tall and lean muscle. I don’t like guys who are overly-muscular, but lean muscle is perfect for me. So about 6’1-6’4 sounds just right to me.
-foxy