The adventuring cleric was always a D&D concept I found a bit odd... why would a holy man go on adventures, usually with a band of thoroughly non-religious ne'er-do-wells in search of gold and glory? Though many versions of many players handbooks throughout the years have mentioned time and again about a cleric advancing his temple/deity/cause's interests, how often does your average DM or player actually do anything of the sort?
Funny, I do believe I heard a cricket, just now.
In my experience, the cleric is typically the only adherent to his deity, or in fact any deity, in a given adventuring party. It always caused me to wonder who actually tends to the temples when the clerics are out adventuring? I have seen it suggested that most priests are 0-level and that only special priest become the spellcasting, undead turning clerics, but if that where the case, would these uncommon and valued members of the temple be allowed to simply meet up with a band of grubby strangers in the nearest tavern and set out into the Wilderlands or wherever? If you think about the level of medical technology present in most D&D game worlds, do you think the powers that be would be keen on the only reliable magical healers stepping out to risk their lives against bandits and orcs?
So, in my campaign I have decided that the kingdom where we lay our scene, Avengard, is dominated by one monotheistic religion: the Temple of Aldurn. Aldurn is a Lawful Good deity who does not recognize other deities as such, but merely as minor demons and celestial creatures unfit for worship. The Temple of Aldurn is very much like the medieval Catholic church. The clerics of Aldurn are temple soldiers and healers, and generally they only go on adventures in the service of the temple. They are not really given any time to start up a freelance adventuring career, and adventures with non-clerics or non-paladins would certainly be forbidden.
However, just because the Temple is the official state religion doesn't mean that other religious orders of other deities don't exist, however, they are not allowed to build temples in the cities, nor are they allowed to gather in more than very small numbers, making it impossible to establish anything other than local shrines in minority quarters or out in rural areas. These groups did (and do) have clerics, who are more free to do as they please. Adventuring clerics, in other words, are those clerics of temples long banned and ousted when the conquering Gahlnic Empire brought the Dictum of Aldurn from the north. In the centuries since Gahln broke apart, many of these forgotten orders have began to emerge once again. Lacking much in the way of structure, many of these clerics have grown accustomed to wandering as lone advocates of their deity.
...and of course, let us not forget the pagan druids, who simply withdrew into the woods and waited for Gahln to pass into history, as every empire of man is fated to do.