The Holy Roman Empire (before Barbarossa just called Roman Empire, since the 15th century called Holy Roman Empire of German Nation) was the foremost European power in the high middle ages, until the interregnum in the 13th century, and a rotting corpse of a legal entity afterwards, especially after the Westphalian Peace 1648. Both phases have attracted considerable attraction by Alternate Historians, even though the only person who really understands the HRE is Susano.
The idea of a continued Roman Empire was laid 801 with the coronation of Charlesmagne. With the disintegration of the Frankish Empire, the title, while still being granted by the Pope, lost significance. However, in 962 Otto the Great of Germany (the East Frankish realm) was crowned Roman Emperor, and with that, the imperial dignity remained in the eastern half of Charlemagne's former empire.
The Holy Roman Empire was on its peaken during its time under the Emperors of the House of (Hohen)Staufen, most prominently Frederick I Barbarossa and his grandson, Frederick II The “Heretics King”. During this time it was feudally organised and thus decentralised, but so was every other realm in Europe at the time. The central authority of contemporary France was even considered weaker. Thus, it is no wonder that many timelines deal with that, often attempting to avoid the dwindling of imperial power. Faeelin's The Prince of Peace and Midgard's Unholy Roman Empire do this. Other timelines in this period are Shadow Knight's Tuscan Sons and Justin Pickard's The Lantern Empires.
Frederick II. concentrated himself on his other realm, the Kingdom of Sicily, and hardly bothered with Germany, where he gave most royal powers to the single princes. The interregnum following his death confirmed this state of affairs. Afterwards, the Empire became increasingly weaker, until the Westphalian Peace 1648 robbed it of nearly all central power. Afterwards, it was seen as an abnomination even by many contemporaries, and Voltaire famously exlaimed: “The Holy Roman Empire is neither holy, nor roman, nor an empire.”, a sentence often quoted or altered in Alternate History.
This phase is significant in Alternate History because of two things: First it gave rise of the great powers inside the Empire: Austria and Prussia-Brandenburg as two of the five great powers of Europe, and Bavaria, Saxony and Hannover as middle powers. Second, the disunited Empire provided constant casi belli and battlefields for European Wars. Near every major German War of the 17th and 18th century was at least in parts also inside Germany (by that time synonymous with HREGN). Due to those both factors many timelines of the period also cover the HREGN, though it is considered a difficult subjects: After 1648, the mechanics of the imperial structrue ebcame so convoluted despite their unimportance, and the dynamics between and details about the single states so complicated that many authors also avoid that period's HREGN like the plague, especially since the anglophone authors will know more about the Great Britain of the time then the Germany of the time.
Nontheless, despite that many members seem to harbour a historic nostalgia about the HRE, or at least some of the single states inside it, especially if it is just maps - maps do not have to explain anything. Hence, in many timelines or maps, the HREGN continues (in its disunited form), or Germany is otherwise disunited - see the Disunited Germany cliché.