Lets say were in the somewhat near future and our current forms of birth control have become more reliable, in particular female birth control is less likely to cause side-effects. The government has mandated that at a certain age (per-pubescent) all children will have birth control implanted which will prevent pregnancy.
To have a child someone must go through certain steps to have the birth control deactivated (for example perhaps a very short parenting class and a small, but manageable even by those who are not rich, deactivation fee, nothing intensive and not used as any subtle eugenics, just enough to ensure they really mean it and put some thought into it first). Lets say that the birth control tends to be reactivated after words, in short your not getting pregnant unless you actively make it happen.
Lets also say that medicinal skills have increased enough to make STD less threatening. I'm thinking that they can be treated, but it may be difficult and somewhat expensive to do so. However, since the treatment would be occurring regularly there is a technological equivalent of herd immunity in effect, the STD have difficulty spreading because their treated so soon after being infected, which in turn makes the society effectively immune even if all individuals aren't.
What would the cultural impacts of this be? Presumably sex would be less of a 'big deal', though I imagine concepts like cheating on your partner would still be quite strongly disproved of; I doubt we would turn into bonobos mating, literally, over a dropped hat.
Would we culturally discuss sex more openly? what would our sex ed for children be like? How would this effect when a child would be considered mature enough to have sex with their peers?
What sexual taboos might still exist?
Will our view of motherhood change now that it has to be a conscious decision? will traditional nuclear families be more or less common? Would we be less forgiving of bad or indifferent parenting if you had to sign up to be a parent? Would we start to have expectations of family size now that one can easily decide exactly what their ideal family size is?
How would we handle those that claimed that birth control was against their religious beliefs? Lets say for now that only one sex gets birth control regularly (presumably women, since biologically that seems like a easier challenge to do reliable and safely). If everyone is trained to assume that all women are on birth control and thus sex is 'safe' would the presence of those who objected to birth control be an issue due to the risk of someone not realizing the risk of intercourse with them? Would we develop some short hand way of indicating who was on birth control and who wasn't? some form of jewelry or clothing etc.
This would also decrease the population, and in particular the presence of unwanted children, which I expect to have a significant impact on society in itself. However, I've asked a second question about that effect: Effect of preventing unintended pregnancy on society