To give more detail about the role of eclesiastical rulers within the HRE: While Bishops (in the shape of the Archbishops, who also function as the Prince-Electors, and the many generic Prince-Bishops definately are the most prominent there a myriad more of princely and imperial abbeys (the german term is Reichsprälat). And like those bishopships those abbeys enjoyed imperial immediacy (meaning that they followed only the orders of the Emperors; in practice having souveranity over their territory) and directly represented themselves within the Imperial Diet. This granted them of course a considerable amount of freedom within the HRE but interestingly they had one very important duty towards the Emperor: the ecclesiastical rulers were amongst the most important military vassels of the early and middle empire.
A famous example is the Reichenau Abby, which supplied Otto I. and Otto II. with many contingents of heavy cavalry for their varios expeditions against the hungarians and saracens.