StarCraft owned and published by Blizzard Entertainment.

Arguably the most popular (and successful) real-time strategy series of all time, StarCraft is all about war. Shifting to a grim future, StarCraft focuses on three species - Terran, Zerg, and Protoss - as they vie for domination in a crowded galaxy. And, unsurprisingly, there may be something far darker and more dastardly pulling the strings in the background...

The StarCraft franchise only consists of two overarching games, StarCraft and StarCraft II. That said, each game is divided up into a series of campaigns, including expansion packs that add to the story. You can normally play the campaigns in any order you like, though if you want to play chronologically you want to go from left to right on the selection screen. This timeline divides them into the individual campaigns, since other media slot in-between some of the campaigns.

Unlike other franchises whose outside media is of variable canonicity, the majority of StarCraft's material is considered canon. So long as material in a novel or comic does not contradict something in the games, it is included on the timeline. (Though if you're only interested in the 'main' story, stick to the StarCraft, Brood War, and StarCraft II campaigns.)

There are many short stories in the StarCraft franchise. These are not currently included on the timeline. (I'll take a stab at it in the future.)

Two expansion packs for the original StarCraft, Insurrection and Retribution, were licensed by an outside company, and not released by Blizzard. These stories don't contradict the events of the other games, but their canonicity is debatable. Given their age and poor reception, you probably don't need to bother with either expansion pack, and they're not included on the timeline.

In-Universe Chronological Order
Release Order (video games)
Release Order (novels)