The Swedish foreign minister, Carl Bildt is of the Noble House Bildt, introduced in the Swedish nobility 1664, but known as Danish nobility since the 1100s (they were included in Sweden when Sweden got previously Danish-Norwegian Bohuslän in 1658).

So here you have a representative of a very old noble house that holds a formal position of power today. He was also Prime Minister of Sweden 1991-1994.

The new king of Spain, Felipe VI, that you might've heard of recently, will probably satisfy you.

House of Bourbon is quite old and famous already. During more than 700 years, they held power in France, Spain, and other places. For example Louis XVI of French Revolution fame was of house Bourbon.

Well, that's not the end of it. They're a cadet branch of Capets. These guys are tracing their lineage to Hugh, the ruler of Franks in the late 10th century.

Karel Schwarzenberg, the former Foreign Minister of the Czech Republic, is the head of the House of Schwarzenberg, who were founded in 1429 when they were granted a Baronial title in German Franconia. He ran unsuccessfully in the Presidential election of 2013, coming second.

Any of these, I suppose.

The Japanese imperial family have been at least symbolic leaders of Japan for nearly 2000 years, with myths continuing the lineage back to 660 BC. However, they currently hold a purely symbolic position in Japanese politics.

I thought you meant literal houses at first but the Burg Eltz castle is lived in by a 33rd generation of the family that built the castle.

Sorry, but as you've phrased this question it is very broad. We don't allow throughout history questions. These tend to produce threads which are collections of trivia, not the in-depth discussions about a particular topic we're looking for. If you have a specific question about a historical event or period or person, please feel free to re-compose your question and submit it again. Alternatively, you may PM /u/caffarelli to have your question considered for an upcoming Tuesday Trivia thread.