Thay is a country in the Forgotten Realms of Dungeons & Dragons that has a long and storied history, having been the subject of multiple sourcebooks since the setting's appearance. One of the more overtly Sword & Sorcery-inspired regions, Thay is a generically "oriental" country that lies to the east of the Sword Coast region where the bulk of the Realms' lore is focused, ruled by a magocracy and full of byzantine plots that ultimately extend to seeking world domination. The region is one of the most long-lived "evil empires" of the setting, under the power of its mage rulers, known as the Red Wizards of Thay. It is visited in Neverwinter Nights 2: Mask of the Betrayer.
Thay is one of the few kingdoms that openly incorporates all "humanoids" into its culture, making it a place where orcs, hobgoblins and gnolls, amongst other, live in relative peace with humans, albeit at the cost of still being inferior to the ruling elite, who are all wizards and thus treat everyone beneath them equally badly. Gnolls in particular tend to be integrated into the city watch, since their powerful sense of smell and natural tracking skills make them very good at finding criminals of all stripes.
One of the traditional key's to Thayan might, and something that makes them more interesting than generic evil empires like the Kingdom of Iuz on Greyhawk, is that they are clever enough to seek power through subtle means; Thay has trading routes that extend over the world, and their merchants use the magical items generated by their wizardly overlords as currency to buy their way into lands that actively hate them, using this to finance an attempt to subvert nations from within. Another thing Thay has going for it is that it actually has some of the most efficient farming on Toril, and not just because of slave labor, being the only ones with large scale plantations instead of just a bunch of disorganized family farms. This renders it a food exporter that many “good” countries would starve without (something that’s never actually addressed post-Spellplague).
After the Spellplague, Thay went pretty much to hell. The Zulkir of Necromancy, one of the eight wizard-kings who lead the Red Wizards, Szass Tam, transformed himself into a super-powerful lich and promptly went crazy, drinking deep of the stereotypical "necromancy is the best" and "the dead are more useful than the living" koolaides. He seized control over Thay and instituted a necrocracy. Many other Thayans have either fled or chose not to return after conquering other lands abroad and then learning Szass had taken control. These "exile" Thayans want Szass destroyed so they can end his necrocracy. Szass tried to achieve godhood, but the ritual was thwarted by a desperate alliance of his enemies; he needs to conquer new, unspoiled territory before he can try it again.
Szass Tam still rules Thay after The Sundering, though he's started accepting non-undead to the higher ranks, albeit only within Szass' personal servants, but this is only because he started fighting the Demon Prince Eltab.
In Dungeons & Dragons 3rd Edition, it was one of the nations covered in the splatbook "Unapproachable East".