Diablo 2 doesnt have the most complex story but if you read everything and the books it does have a lot of depth and its a logical world (no inconsistencies in lore)
God dammit, I just typed the whole story out and I got a load error. Very short version inc:
-=- Diablo -=-
Diablo has 2 brothers, Baal and Mehpisto. world is split into 3 planes (Hell, Heaven, Sanctuary)
Diablo infests a town, takes over body of the king, 3 heroes try to stop him; warrior, wizard, rogue.
Warrior manages to beat him, but because the brothers are caught in a soulstone they need a new host; warrior crams it into himself to contaminate the demon.
-=- Diablo2 -=-
Rogue and Wizard are corrupted, helps evil now; Warrior is very confused/corrupted and is looking for his bro's.
Diablo/Warrior find Baal who has corrupted his archmage-host (so he is even more dangerous then normal) they imprison they archangel trying to stop him (Tyreal)
We free Tyreal, but diablo+baal are long gone to kurast to find mephisto.
Mephisto corrupted his host (pattern there) opens gate to hell, diablo transforms from human host into himself again and enters hell.
We kill Mephisto, take his soulstone.
We enter hell, smite the soulstone on the hellforge thus banishing their mind to some sort of limbo; we kill diablo and shatter his soulstone.
-=- Diablo2: Lord of Destruction -=-
Baal went to Mount Arreat to find the Worldstone (Sanctuary is the middle of the 3 planes, if that stone is gone hell has free acces to our world)
We get seal-of-approval from ancient barbarian half-gods; kill baal.
Tyreal comes in, sees the Worldstone is corrupted and decided that its better to blow open the barrier than to make it a one-way entry.
-=- Diablo 3 Trailer -=-
Hell is marching, something is apperently cast out/send to help us from the High Heavens.
Oh and here is a .gif of Tyreal because he is THAT awesome