Frankly, it depends on when you're talking about. I can't speak much for the medieval Holy Roman Empire, but the early modern HRE was definitely closely interconnected in terms of Imperial institutions. To quote a previous post I made on this topic:

...the Habsburg Emperors, while afforded a great degree of prestige and majesty by the title of Emperor, did not directly rule the Empire. Instead, the Emperor ruled through the various Princes of the Empire, rather than a central Imperial administration of some sort. It's popular to say that the HRE was, "neither Holy, nor Roman, nor an Empire," and to imagine it as merely a collection of squabbling polities, but that misses out the extensive presence of Imperial institutions. Do note, that while these institutions existed they were not an Imperial bureaucracy nor legislature. The Reichstag provided an institution to acquire a general consensus amongst the Princes, while the Peace of 1495 led to the creation of a court system that could hear disputes between princes and to determine the extent of the Emperor's own powers, (the Reichskammergericht and Reichshofrat respectively.) The Imperial Circles provided a way of common defence, as well as regional bodies for dispute settlement and discussion. The Reichstag regularly voted taxes to the Emperor so that he could provide for the common defence. The HRE was not a unified state as the Kingdom of France, Sweden, or the later German Empire was, but it definitely had its own systems in place. However, these systems were cumbersome and took time to navigate, as almost everything would ultimately require consensus. Moreover, the various Princes of the Empire held rights and privileges within the Imperial structure. As noted, while the Emperor had extensive powers, attempts to infringe on these principles of 'German liberty' as they were termed through Imperial proclamation often met with significant resistance. The Reichstag did enact a great deal of legislation, and the Imperial courts did generate an extensive jurisprudence...

Now, of course, the HRE being what it was, the exceptions to the rule almost outnumber the rules themselves. There were territories within the Empire that were less closely tied to the Emperor. The Swiss and Italian territories were not part of the Imperial Circles, and the Swiss were granted independence in the Peace of Westphalia. It's difficult to give a full answer, as the relationship of the Emperor, the Imperial institutions, the Princes, the Knights, and the Free Cities varied widely, almost on a case by case basis. The Princes were free to rule their territory as they saw, but disputes could be brought to the courts to be settled, but some princes had privileges of non-appeal, and so on and so on. What can be said is that the Princes of the HRE--at least the German ones--were tied together via legal structures in the Holy Roman Empire. While each Prince had a great deal of autonomy, it was not full 'sovereignty' in the sense that we know it today.

Disregarding the question of whether these polities in the early modern can be called 'states', the most important were the seven electors: the Archbishops of Mainz, Trier, and Cologne, the King of Bohemia, the Duke of Saxony, the Count Palatine on the Rhine, and the Margrave of Brandenburg. However, while being an elector gave you a great degree of political power, it didn't necessarily come with hard power, and there was not necessarily a correlation between political importance and physical size and power. For example, the Archbishop of Mainz was the Archchancellor of Germany, and one of the most prestigious positions within the College of Electors, yet he only ruled a territory of ~100,000 citizens. On the other hand, the Dukes of Bavaria ruled a much larger and wealthier territory, yet did not hold an electoral dignity until the title was stripped from the Palatinate and given to Bavaria. The Archdukes of Austria, despite being the most powerful of the Imperial princes, never held the electoral dignity themselves--although they 'gained it' by also being the King of Bohemia. Thus, onto the list of key states within the HRE you can add the Duchy of Bavaria and the Archduchy of Austria, who--after 1526 was also King of Hungary and Bohemia--served as Holy Roman Emperor in an almost unbroken chain from 1440 to the end of the Empire. There are, of course, many other important entities within the HRE, but I do think that covers many of the most important. This of course ignores foreign rulers with holdings in the HRE.

Hopefully, this helps to answer your question, and feel free to ask any follow ups!