The original Diablo was rather light on character back story. You were a random hero who was in Tristram to put down some skeletons, and along the way you decide that killing the guy in the basement is a good idea too. But who were you? Who was this stalwart fighter, shadowy rogue, or enigmatic mage?
Are there any stories or details, canon or otherwise, that explains who the original hero of Tristram was prior to arriving in Tristram?
All that information was provided in Diablo's manual, both who each is and what their motivation might be.
The Warrior:
The Warriors of the lands of Khanduras are well trained in all of the weapons of war. Ranging from crusading paladins to unscrupulous mercenaries, Warriors can be found wherever there is conflict amongst their countrymen. Many of these adventuresome men joined with King Leoric's army and went to battle against the Northern kingdom of Westmarch. As the fires of war burned themselves out, these Warriors returned home to find their kingdom in shattered disarray.
Dark rumors of the mysterious demise of King Leoric abound and the evil that lurks within his Cathedral has drawn many Warriors to Khanduras seeking fortune and glory. ... Whether they are driven by valor, honor, madness or greed, new Warriors arrive in Tristram every day, ready to challenge the dark unknown that awaits them beneath the earth.
The Rogue:
The Sisters of the Sightless Eye are a loosely organized guild shrouded in mystery amongst the peoples of the West. These highly skilled archers employ ancient Eastern philosophies that develop an "inner-sight" that they use both in combat and to circumvent dangerous traps that they may encounter. Known only as wandering Rogues in the West, the Sisters conceal their secret affiliation by posing as simple travelers. Many pompous fools have made the mistake of underestimating these steel nerved women in combat and paid a terrible price for their vanity.
The strange events transpiring in Khanduras have caught the attention of many of these Rogues. They have come from as far as the Eastern dunes to test their skills against the dark evil that is said to be lurking in Tristram. It is also believed that untold riches wait to be discovered among the ruins of the Horadrim monastery.
The Sorcerer:
Although practitioners of the mystic arts are scarce within the often superstitious and religious lands of the West, many magi have made the pilgrimage from the Far East to see for themselves what horrors lie beneath the ruined Cathedral of Khanduras. The veiled Brotherhood of the Vizjerei, one of the eldest and most dominant mage-clans of the East, has sent many of its acolytes to observe the dark events unfolding in Khanduras first hand.
The Vizjerei, known for their brightly colored turinash -or spirit-robes have taken a keen interest in both gathering knowledge of demons and seeing them slain. The Vizjerei elders hope that their acolytes will learn the secrets of the dark evil that they sense growing in the West and can destroy it. The possibility of discovering long-lost tomes of magical knowledge within the confines of the labyrinth has also captured the interest of many wandering Sorcerers.
Beyond that it was left a bit vague, so you could project your own motivations on the character. That was the very slight "RP" part of Diablo being an RPG.
As the other answers state, the Lore was very much not present in the first game, but exploded in the second. The only hard link to any of the PCs actually being a character in the game's lore is Ogden's introduction:
Lore from the manual of Diablo II established that the warrior character from the first game was unknown to the village, despite Ogden apparently knowing him as per his greeting quote. The issue was 'solved' in a sense by lore developed for Diablo III, which established that the warrior was Aidan, known to Tristram, and thus apparently to Ogden as well.
So, this information was not present in the first game. The PCs were simply known as "the Warrior", "The Rogue" and "The Sorcerer". Their characters were then later added to link them to specific characters in the Diablo story.
The "Hero that defeated Diablo" was retconned into Aidan; son of Leoric (Diablo's first victim) and brother of Albrecht (Diablo's initial vessel). Aidan had been sent to War by his father, due to his madness, and returned after Leoric's death, at the beginning of the events of Diablo 1. The idea is that he was the one that became convinced the only way to contain Diablo was to shove the Soulstone into his own head, which ultimately turned out to be Diablo's influence, making Aidan believe it to be that way.
The Warrior of Diablo I eventually became the Dark Wanderer that featured in Diablo II. Diablo III and supporting material altered his backstory to make him Aidan, the son of King Leoric. This was a retcon from previous lore, which established that the Warrior was a stranger to the people of Tristram.
While Aidan was the one to become the ultimate victim of Diablo, turning him into his vessel, leading to the Events of Diablo 2, the others would not return from the depths of the Cathedral unscathed. The evil powers within the Cathedral were so strong that it ultimately affected the other two as well.
Blood Raven (originally known as Moreina) was a member of the Sisterhood of the Sightless Eye. She played a role in Diablo's defeat during the Darkening of Tristram, but fell into Hell's thrall in the aftermath.
While not corrupted in the same manner as Moreina (who was turned into a demon), Jazreth instead fell to madness, eventually becoming the Summoner in Diablo 2.
The Summoner (previously named Jazreth) was a powerful sorcerer. Once a member of the Vizjerei and opponent to Diablo, he fell to evil and was struck down by a new group of heroes.
As for the future of each character The Warrior becomes the Dark Wanderer, eventually Diablo. Source.
The Rogue, is Bloodraven who is driven mad and becomes Andariel (the Act 1 boss). The Sorcerer, is The Summoner who you fight in the Arcane Sanctuary in Act II. This source speculates on the Rogue becoming Blood Raven, and the Sorcerer becoming The Summoner.
So they all lived happily ever after.
From the Diablo III wiki:
The Dark Wanderer is established in background materials for Diablo II as the warrior from Diablo I. In the Book of Cain1, he is given the name "Aidan" and is revealed to be the the eldest son of King Leoric.
It appears as though Aidan took his group, possibly containing other Warriors, as well as the Rogue and Sorcer down to hell with him.
A group of heroes- a Vizjerei sorcerer, Blood Raven the Rogue captain, and Albrecht's own brother, Prince Aidan- entered the darkened Monastery in an attempt to find and rescue the Prince. Unwilling to give up hope, the heroes sought out, encountered, and eventually vanquished the Lord of Terror himself.
I'm trusting the Wiki correctly quotes from the book or at least paraphrases correctly. dlanod is still correct, in that the heroes Aidan mustered are as he describes, and it's likely that Aidan himself is a 'warrior of Khanduras' and 'returned home' fro mthe war much like Lachdanan did.
1. Book of Cain on Amazon
