Because of the many differences that exist between American and Japanese manner, my wife and I have been exerting a great deal of effort to learn Japanese manner, not particularly because we want to be Japanese, but to avoid standing out as "rude gaijins" and to make it easier to make good friends.
One custom that we are learning in Japan is the art of gift giving. It seems that whenever one party visits another, they always bring a small gift, as if it were meant to be a "repentance offering" for invading -- or at least entering -- another's territory.
Gifts, or o-miyage, suitable for this ritual are usually small trinkets or quickly consumable, and are usually not meant to be of any use to the recipient. Thus, some fruit or perhaps a toy for one's children, make appropriate o-miyages. Usually, when handing over the gift (always with two hands, no matter how small the gift really is), the visitor says something to negatively criticize his gift, such as "Makoto ni tsumaranai mono desu ga..." ("It is truly a trifling thing, but...") However, I have yet to observe the giver actually criticizing himself or his generosity, rather than the gift.
Gift giving has the effect of softening the abruptness that exists when the visitor first arrives, and provides subject for alternative conversation if it appears that the initial conversation might proceed lamely. It is also quite common for the recipient to share his gift with those around him or with the giver himself, if the nature of the gift and the circumstances of the visit permit it.
For this reason we were encouraged before coming to Japan to bring a bunch of token American o-miyages. Because the Japanese don't necessarily expect Americans to act Japanese, it would not be horrible to never give o-miyages. However, when gaijins take advantage of the opportunity to give gifts, the recipients are usually flattered and surprised. They end up feeling a lot more comfortable with their new gaijin acquaintance because the gaijin has shown a desire to cross the cultural boundary that exists between them.