/u/atropicalpenguin

This is a great question. At its dissolution in 1806, some were shocked and most were saddened by how things turned out. Several parties, such as Sweden and Prussia, insisted that Francis had the right to abdicate but he had no right to dissolve the HRE. Thus, it still existed in theory. Certainly, legalities and nostalgia were major issues, and Austria both fought to retain the imperial symbols and also willingly paid pension to former courtiers of the HRE.

So when the Congress of Vienna started in 1815, many did expect the HRE to be revived in some form. But there were several complications. Over 300 of the entities that used to comprise the HRE had been destroyed. So there were arguments about the structure of a hypothetically revived HRE -- who were the immediate states and who were the the mediatized states? -- what was to be the new system? Not that everybody wanted to be elevated to higher posts, as many minor states preferred to return to a mediatized status to reduce their risk and responsibility.

But the biggest issue was the new balance between Austria and Prussia, and the larger fiefdoms. The larger principalities demonstrated that they had military strength unseen prior to Napoleon's wars. So most proposed a new federated HRE.

The outcome of this was the German Confederation, into which Austria, Prussia, and the four kingdoms were members, along with grand duchies, principalities, and free cities; a total of 39 member states. Each of these members were considered sovereign states, with federal rights and responsibilities. This Confederation hewed to nostalgia of the HRE, but in practice it was a dis-empowered body. The Habsburgs retained their hereditary rulership (now called Präsidialmacht, presidency of the assembly) although now its true power has become even more symbolic.

This created problems in territories formerly within the HRE but now not contained in the German Confederation, in particular those in Italy. It eventually led to the Italian unification, and the Confederation more German in character.

This German Confederation survived the revolutions of 1848, although its inactivity demonstrated that it was powerless. In 1866, Austria and Prussia fought over control of Schleswig-Holstein, which they had wrested away from Denmark as allies under pretext of protecting ethnic Germans in those territories from being absorbed into Denmark. Austria pressed its case through the Confederation's Diet, which ruled against Prussia when the latter annexed Holstein. Thus, most German states sided with Austria as Austria declared war. However, Prussia prevailed, and Bismarck dissolved the German Confederation in favor of the North German Confederation dominated by Prussia.

Later on, the German Empire of 1871 was an expansion of this North German Confederation: it was renamed The German Empire and additional states south of the Main entered into membership thanks to Bismarck's deft diplomatic maneuver to goad France into declaring war against Prussia. The larger of these states, such as the kingdoms of Bavaria and Württemberg, retained a privileged status and a large degree of independence.

Austria, naturally, refused to be a member.

Want to know more? Wilson's The Heart of Europe has some great material, as does Wawro's The Franco-Prussian War.