Living in Western-Europe, the notion of belonging to a clan, tribe, or any other kinship-relation which extends beyond the immediate family is entirely foreign. However, from what I understand Germanic tribes did have 'clans'. When and why did these disappear?

by Congracia
ConteCorvo

I would not say that Western European cultures never possessed a kinship-based relation influencing social and political dynamics of its history.

It's true that Germanic migratory populations (Langobards for example) organized their movements in groups based on a family basis, known as farae (sing. fara), but also during the XII-XIV centuries, the city states of central and northern Italy saw a great amount of families and clans (although this latter word is not part of Medieval Italian lexicon) populating the cities and organizing the political life around the loyalties they possessed among the many family branches both inside the urban zones and in other locations. An example could be Florence, where banker families such as Scani, Cerchi, Strozzi, Spini and others almost monopolized the political struggle between Guelphs and Ghibellines during the 1200s and 1300s.

Many cities throughout Italy had local political power at least influenced by noble families organized by blood ties and factionalism. Cities like Naples, Capua, Aversa and many others in the Kingdom of Naples during the Aragonese period and perhaps even during the times of the Angevin dynasty, had several urban districts where the palaces of these families were located and where these groups would have a sort of meeting hall, called a seggio, "seat" where nobles from a district, mostly belonging to the same family or with strong family ties, would hold meetings and decide about the city's politics and also plausibly to organize the exaction of the indirect population tax (collectae, "collective [taxes]").

Outside the urban context, rural areas were virtually entirely based on family ties and bonds. Where lands were held either as a hereditary concession to a dynasty or as a bannal lord who forcibly seized power in a given area, the vassalatic structure used to maintain and administer these lands was largely composed of relatives of powerful individuals such as a count or baron. This is most clear if we look at the names of famous royal families throughout European history. Norman rulers of both northern France and southern Italy were of the Hauteville family, to the point of creating two branches of the same family. The Angevin rulers, originating from the county of Anjou in Provence, had ramifications both in southern France and southern Italy with the kingdom of Naples which they seized in 1266, but also created another branch located in Central Europe as the Anjou-Durazzo dynasty ruled Hungary from almost the entirety of the 1300s.

Ultimately, I would say that this tendency perhaps died out when the ideal of the old European aristocracy ultimately disappeared after WW1, but it's a personal conjecture.

I hope this answer helps you.