Sidle , you took the words right out of my mouth (substitute brown eyes, olive skin and champagne-glass chi chis…).
My situation might be a little different, however, in that I’m Black, but grew up around a lot of White people, which means that among certain people I got little attention for my looks, and among others I got ALL the attention!
While the (White) boys I knew growing up thought I was pretty groovy, and I enjoyed a modicum of “popularity” in terms of getting invited to parties and all, come prom time I was pretty much left out in the wind. (Now that I’m in my 30s, I’ve come across a couple of fellas from my past who’ve admitted they had big crushes on me back in the day… then sort of evaded the issue when I asked where the hell THEY were on Prom night, when I was eating Chinese food with my mom!)
On the other hand, I always got a lot of attention from Black people old and young (friends of my parents, or the kids in my grandparents’ neighborhood/church in Houston, where I spent the summers growing up, fellow students at the Black college I went to…) for my looks (which may have saved my ego during those promless adolescent years). Sucks to say, but light skin and long hair were my “in” to the Beauty Hall of Fame among Black people, in those days (and HOO-WEE! just let me MENTION cutting my hair in those days, Honey, a full-on intervention took place)…
Ironically, nowadays I find that more of the Black people in my life are rejecting the “lighter and longer” aesthetic that garnered me all those dates in college, and are more attracted to dark-skinned people (I am strangely happy about this…), meanwhile more White people are asking me out on dates these days (OK, not LATELY, but everyone has a dry spell, right?) ; did I mention I ended up dating (in my mid-20s) one of those guys who had a crush on me in high school?
I swear to God, though, if one more person tells me I look “exotic” (honey, I’m just a Colored gal from Kansas), I will kick some neck up in here, you hear me? 
But I digress.
I often wonder how people (no matter where they rank on the “Magazine Standards of Beauty” scale) can live day to day thinking, “I’m ugly.” It’s one thing if you’re thinking, “I’m no Christy Turlington” and you don’t give a rat’s ass (as you shouldn’t), but I do see the point of the original OP, and echo the sentiment: How DO you cope if you think you’re butt-ugly (which, as someone said, few people are) and are hating yourself because of it?
I feel like I’ve been lucky in that I’ve never been put into a situation to know what that’s like, but I wonder what others think about who’s to blame, here?
Can we pin it on the media (whose new emphasis seems to be on the “BUT” campaign: “[Fill in appropriate “Beauty Infraction” here] BUT still beautiful”), or do we say, “Well, hell, all of those people trying to convince us we’re ugly are just doing their jobs, which is to sell us things that promise to make us pretty, ,and it’s our fault if we fall for that crap?”