I completely fed both my girls out in public. Moreso my second as I was a bit braver. Heck, I even had a young stock boy find me a chair to sit down on in the middle of the grocery store when she was 3 weeks old. Baby's gotta eat. Better that then screaming at the top of her lungs.
I completely agree with Becky's comment, it seems crazy that with all the fashions that people insist on wearing and all the nudity in the media that breastfeeding is still perceived as obscene. Crazy! Go for it, although I think sometimes a modesty shawl, blanket or one of those muslin cloths that babies never seem to be without is a good idea. Cosier, warmer and a little bit of privacy from all the idiots who apparently never knew that that is why women come with breasts! ;)
No one finds it disgusting when a women walks around half naked at the beach or shows tons of cleavage with a low-cut shirt, so why are using your breasts for what they're made for so disgusting and controversial? Seriously, you can see way more boobs in 10 minutes of primetime TV than you can when I feed my daughters!