When Kaddish was only the demarcation between the various parts of the service, there were initially seven Kaddishes in the liturgy; three in the morning service, and two each in the afternoon and evening service, for a total of seven. This was connected with the verse: "Seven times a day I praise you for your righteous laws" (Psalm 119:164).  

When the custom arose in the thirteenth century to recite Kaddish for the dead, it was initially seen that the one saying Kaddish was momentarily the prayer leader, therefore only one person could say Kaddish at a time. As often there were many mourners present, especially in a large community, accommodating everyone was a problem. Therefore, many additional Kaddishes were instituted, after every scriptural or Talmudic reading in the prayer book. As many as twenty Kaddishes are recited in some communities.  

When Sephardim adopted the idea of saying Kaddish for the dead, they altered the custom to have all the mourners say Kaddish in unison. This spread to Eastern Europe as well. However, in many communities it became standard to have each mourner say Kaddish at his own pace, resulting in a cacophony of unintelligible sound. Many rabbis have condemned this practice, but one still finds it often.  

Most German, and some Central European communities, still follow the custom of only one person saying Kaddish at a time. Rules were set up for a hierarchy of those reciting Kaddish: those saying for a parent come first, those in the first month of mourning have precedence over those past that time, etc. In a very large community, an individual mourner, especially if saying Kaddish for a different relative (sibling, spouse, child), might only get to say Kaddish once every few days, or even never.  

But how often does one need to say Kaddish? Some say once a day is sufficient. Some say that one should say Kaddish at each service at least once, making for three times a day. (This was the practice of ARI z"l). Some insist on eighteen times a day. Although there is some basis for this in the Zohar, ARI z"l declared it a mistaken custom. Nevertheless, some still do this, especially Chabad. In any case, this has resulted in different numbers of Kaddishes in different communities.  

Opinions differ if one person can say Kaddish for more than one deceased individual. One can see people with lists of dead people, having them all in mind when saying Kaddish. Some even do this for a living, saying Kaddish on behalf of those who need to say Kaddish, but cannot attend synagogue. Rav Moshe Feinstein wrote that one cannot say Kaddish for more than one person at a time. He recommended that one saying it for many people should "get in" one Kaddish a day per name. It is difficult to make rules in this area, as it is a relatively late custom, with no sources. Any "rules", will be based on local practice rather than actual halachah.  

A more modern controversy is the question of women saying kaddish. That will be my next topic