TJ says
Depends on the amount of buttons and vents I would have thought. Double breasted looks best buttoned. Single – leave the top and bottom button undone – unless its a single button jacket in which case the button should be done up
Wiki says
Buttoning the suit jacket
The buttoning of the jacket is primarily determined by the button stance, a measure of how high the buttons are in relation to the natural waist. In some (now unusual) styles where the buttons are placed high, the tailor would have intended the suit to be buttoned differently from the more common lower stance. Nevertheless, some general guidelines are given here.
Double-breasted suit coats are almost always kept buttoned. When there is more than one to fasten (as in a traditional six-on-two arrangement), only the top one need be fastened; in some configurations, the wearer may elect to fasten only the bottom button, in order to present a longer line (a style popularised by the Prince George, Duke of Kent).
Single-breasted suit coats may be either fastened or unfastened. In two-button suits the bottom button is traditionally left unfastened except with certain unusual cuts of jacket. When fastening a three-button suit, the middle button is fastened, and the top one sometimes, but the bottom is traditionally not designed to be (although in the past some jackets were cut so that it could be fastened without distorting the drape, this is not the case with current clothing). A four-button suit is untraditional and so has no traditional guidelines on buttoning, but the middle ones at least should be fastened. Additionally, the one button suit has regained some popularity (it is also a classic style for some Savile Row tailors). The button should always be fastened while standing.
With a single-breasted suit, it is proper to have the buttons unfastened while sitting down to avoid an ugly drape. A good double-breasted suit is usually able to be left buttoned, to avoid the difficulty of constantly redoing inner buttons when standing up.