1. A system including at least first and second portable information processing apparatus each having corresponding apparatus identifier information associated therewith and each configured to selectively execute one or more applications, the first portable information processing apparatus comprising: a first processing system; a first memory storing first data associated with a first application executed by the first processing system, the first data being usable by a second application executed by the second portable information processing apparatus; and a first wireless communication module operable in parallel with the first processing system and comprising a second processing system configured to execute a communication process for determining when communication with the second portable information processing apparatus is possible and for sending the first data to the second portable information processing apparatus and/or receiving second data from the second portable information processing apparatus when communication is possible, wherein the first memory further stores apparatus identifier information associated with one or more other portable information processing apparatus with which the first portable information processing apparatus has previously established communication, and the second portable information processing apparatus comprising: a third processing system; a second memory storing the second data, which is associated with the second application, the second data being usable by the first application; and a second wireless communication module operable in parallel with the third processing system and comprising a fourth processing system configured to execute a communication process for determining when communication with the first portable information processing apparatus is possible and for sending the second data to the first portable information processing apparatus and/or receiving the first data from the first portable information processing apparatus when communication is possible, wherein the second memory further stores apparatus identifier information associated with one or more other portable information processing apparatus with which the second portable information processing apparatus has previously established communication, wherein the second processing system executes the communication process of the first portable information processing apparatus regardless of an execution state of the first application so that the first data can be sent to the second portable information processing apparatus and/or the second data can be received from the second portable information processing apparatus even when the first application is not executed by the first processing system, and wherein the communication process of the first portable information processing apparatus does not send the first data to the second portable information processing apparatus if apparatus identifier information associated with the second portable information processing apparatus is stored in the first memory, and wherein the third processing system executes the communication process of the second portable information processing apparatus regardless of an execution state of the second application so that the second data can be sent to the first portable information processing apparatus and/or the first data can be received from the first portable information processing apparatus even when the second application is not executed by the third processing system, and wherein the communication process of the second portable information processing apparatus does not send the second data to the first portable information processing apparatus if apparatus identifier information associated with the first portable information processing apparatus is stored in the second memory.