I think that you could say marital alliances were hugely important within papal families. You've already cited an example from The Borgias (sensationalism aside, it doesn't stray from history too much), and that type of dynasty building was far from uncommon with other papal families before and after them. The Pope's relatives, associates, and especially any illegitimate children he might have, were extremely important players in the political world both in the Italian states and across Europe, just as with any other royal family. Except, we're not talking about just any royal family... We're talking about THE family that headed THE church. The amount of power the family as a whole held when one of their relatives was on the papal throne was immense.

As for not being able to inherit the papacy, well... There were definitely dynastic papal families. A good example is the Medici, who had a lineage of four popes in the 16th century that were all related:

Leo X (1513-1521) Clement VII (1523-1534) Pious IV (1559-1565) Leo XI (1605-1605)

Though they didn't pass the papacy directly from one to the other the way a traditional inheritance would work, the influence of the Medici family was such that they were able to secure the papacy a number of times (yes, this is definitely an implication that they bought the papacy whenever they could manage it). And the Medici were by no means the only family buying the votes necessary to secure a papacy.

Other papal families included the Colonna, della Rovere, the Farnese, the Orsini, to name a few of the more notable clans.

If you're interested in reading material on the subject, there's loads to chose from. Two books I can recommend look at this from the female perspective:

Lucrezia Borgia: Life, Love, and Death in Renaissance Italy by Sarah Bradford.

Mistress of the Vatican: The True Story of Olimpia Maidalchini: The Secret Female Pope by Eleanor Herman (godawful sensationalistic title aside, this is an excellent read and very well researched).