The term for baby-like features is "neotony", and it's been recognized as being a major influence on what humans have evolved to recognized as "cute". Probably a survival instinct - the more babies are cared for, the better the survival for the species which has those genes.
An example of this is in Japanese animation and comics, particularly the Chibi (child) form like Hello Kitty. The roundness of heads is also part of why puppies and kittens are cuter than adult dogs and cats.
This generally has to do with facial features, not the concept of roundness itself. Consider that a volley ball is not particularly cute to anyone, even though it is the embodiment of roundness. In other words, it must be something that you recognize as a face first, and have roundness second.
As for breasts, there are a number of possible reasons why they might also be something that humans are wired to find attractive. One of the main reasons pointed out by anthropologists for believing that there is such an innate human reaction to female breasts is simply the fact that humans are the only animals in which non-functioning breasts (that is, not currently being used for feeding) are prominent. In all other animals, breasts are essentially the same in males and females, until the female becomes pregnant - only at that point do they grow and become different.
The counter argument to that is that human women grow breasts as part of normal puberty to camoflauge external signs that they are pregnant. This allows women to basically mate with more than one male, each of whom is unaware if, or when, she became pregnant. She could be provided for by several men while keeping multiple relationships a secret.
However this is counter to female behaviour when it comes to relationships. Although both men and women in all societies studied have affairs in secret (effectively poligamy, without calling it that), men and women have affairs for different reasons. In general, men simply crave variety, and affairs are basically filling in needs that they don't get from an existing relationship. They see this as a more or less permanent or open-ended situation. Women, on the other hand, tend to have affairs as a bridge between leaving one person for another (women who are part of a man's affair often are waiting for him to leave his wife, assuming men are the same as women, and are disappointed if this doesn't happen).
Given this tendency, it's not so likely that breasts exist in order to allow women to have affairs, as their behaviour indicates this is not what women have done as humans evolved. An alternative is simply that since the primary interest for males is to spread their genes, the typical male behaviour is to stop once a woman is pregnant, and move on to another. If a woman shows no signs of being pregnant (that are obvious enough for a man to notice), he will remain a mate and provider for a longer period - eventually evolution would encourage this parenting behaviour, so that men would want to be long term providers for the women, and their children.
It's still possible that breasts are along the lines of peacock tails or the swelling of babboon bottoms - men liked them, and women who have them got noticed more, and had more children who passed on both the genes for large breasts in women, and for enjoying large breasts in men. There is nothing saying that breasts can't have more than one effect on human behaviour and evolution.
However, the reason for the appeal of breasts then is only the fact that they are breast-shaped. They would be attractive no matter what shape they actually had - take a look at the shape that babboons find attractive, in the photo at the top of this story:
In that case, if breasts looked like sacks of potatoes, then that would be the standard of beauty or sexy.
There are those who think that the shape of breasts as they are is due to the fact that human ancestors, like almost all other animals, mated from the rear, and so it's likely that the biggest turn-on to a male was the shape of a woman's ass. The development of bottock-shaped breasts encouraged a front-to-front mating position, which encouraged more personal interaction between early humans during sex, which finally created a closer emotional bond which led to family-oriented units which could provide more resources for raising children, as well as the basis for human civilisation.
A bit of a long chain of events to explain things. It's possible that a number of factors converged by coincidence, and the end result is both breasts and human civilization. Nothing definite is known, but as usual, everyone has their theories (feminists have some intersting thoughts too).