I don't see a problem with breastfeeding in public if the woman is discreet and covers up, and the purpose of doing it is to feed an infant. If anyone's bothered by the mere *idea* of breastfeeding an infant, even though they don't actually have to see anything, well, they need to get over that.
I do have a problem with people who just whip out a boob, without making any effort to be discreet (for the record, I am equally grossed out by people's boobs hanging out of their tube tops and such as well, that's nasty too) - yes, they have a right to feed their child, but they also have the responsibility to be respectful and considerate of others who don't want to see a stranger's saggy, strech-marked post-pregnancy and breastfeeding boob hanging out in public - to their credit, 99% of women I've seen breastfeeding in public have been great about covering up; I've only ever seen one just yank her top up and let it all hang out, and that's just further proof that anyone who's unwilling to cover up is simply disrespectful, or else just plain immodest and lacking in self-respect, because if the vast majority of women manage to breastfeed in public without letting their entire breast hang out for everyone to see, it obviously can't be too horribly difficult to be a bit discreet, and the only reason anyone wouldn't want to is because they either don't care at all about anyone else, or are some sort of exhibitionist.
I also have a huge problem with people who breastfeed in public with the express purpose of calling attention to themselves or making a point, like those who take part in 'nurse-ins' - by all means, if your baby is hungry and you happen to be in public, breastfeed, but doing so purely to garner attention is just so terribly tacky.
Finally, while I think that breasfeeding a *baby* in public is perfectly fine given a bit of discreetness, breastfeeding a child of two, three, or even older in public is disgusting and absolutely unnecessary. A baby cannot be fed any other way (assuming one does not bottlefeed), so the options are breastfeed or let the baby go hungry, the latter obviously not being a reasonable option, but a child of 2+ can easily be fed a snack such as fruit or crackers or juice or whatever, or even a meal in a restaurant when in public - when someone is breastfeeding their three year old in public, again I tend to think they are doing so to make a specticle of themselves or to prove a point or make a political statement, etc. (which as I said above, I think is totally tacky) because there is no earthly reason a child of that age *needs* to be breastfed in public.