IME no, not at all. There can be parts which could be described as painful but they may not happen to you, and in the normal course of things it's not painful at all.
The bits I've found uncomfortable:
At first when they are newborn there can be a little sort of ouch as they latch on, makes you breathe sharply. This should last for no longer than 10 seconds at the start of the feed and about 10 days max, then it completely goes away.
After birth breastfeeding causes contractions which is your womb going back to normal size. I think you get these anyway, but when breastfeeding you tend to associate it with feeding because that's when you notice it. Again it's only for the first couple of weeks or so. Also I never found these very bad, similar to mild period cramps although other people I know report they were worse.
When your milk comes in, or later if you have a long gap between feeds, and you get engorged that can be painful although again it only lasts a day or two. Feeding or expressing immediately relieves the discomfort. You will likely experience this whether you breastfeed or not (obviously if you do, it might happen more than once). Engorgement not dealt with or noticed can cause mastitis which is infection of the milk duct which is quite painful, but might not happen to you. I only had it with my second child. It is treated with antibiotics. Was not the worst illness I've ever had although not very nice.
When they are older occasionally they bite which is unpleasant. It tends to be a short lived phase.
When they are huge if you breastfeed until they are that long they can climb over you and elbow/chin you in the boob which isn't very nice! But you might stop before the gymnastics become an issue.
I never had thrush, badly cracked nipples etc, those things don't always happen.
The vast majority of feeds have been completely painless and just a neutral feeling.