Many of my juices are good right after I make them. Fruit flavors are a good example. It depends on the juice. I made a lemon meringue pie juice, and it was great right away, but the longer it sat, the more the lemon flavor diminished. I altered the recipe, and now I just have to let it steep after making it. Yes, coffee, vanilla and cream type juices benefit from sitting for a while.
As far as commercial juice goes, I got 120ml each of vanilla bean ice cream and strawberries and cream from a vendor which were both pretty good right when I got them. After a couple of weeks, they have become absolutely delicious.
As a general rule, if the juice tastes like {censored} to begin with, letting it sit probably won't help it much.