Given that she lives with two sinister Siamese cats, and has a problem with spiky sweetgum seed pods showing up in her house in unexpected places, I think it’s a matter of when blood will be shed, rather than if. 
My cats are royal PsITA.
The situation is complicated by the fact that “prince”, in some european countries, is a title of nobility, but doesn’t necesasrily indicate membership of a current or former ruling family. For example, the King of Italy (and the rulers of some of the Italian states which preceded Italian unification) might confer the title “prince” in the same way that they might make someone a duke or a baron or a count. And the same was true in many other countries. There are probably huge numbers of people who use, or are entitled to use, or were entitled until a republican government abolished the right to use, “prince” as a title of nobility, but only a relatively small group who enjoy the title because of descent from a sovereign ruler.
Negative. Per a grand ducal decree in 1995, the title of Prince/Princess of Luxembourg is limited to children of a grand duke or duchess, and the children of the heir to the throne. Other male-line descendants bear only the title of Prince(ss) of Nassau. The children of Princess Margaretha’s eldest brother, Grand Duke Henri, are “of Luxembourg,” but the children of Margaretha’s younger brothers and the children of Henri’s younger sons are “of Nassau.” The children of Margaretha and her sister take their style from their respective fathers, and are not considered to be of Luxembourg. In fact, the sisters and their children are not in line for the Luxembourgish throne either; absolute primogeniture applies only to the descendants of Grand Duke Henri. Previously, Luxembourg followed a version of semi-Salic law, in that females were eligible only if every single male in the entire dynasty was dead (which happened in 1913).
(A couple of the grand duke’s cousins, born long before 1995, are “of Luxembourg,” but their children are not.)
So Prince Josef-Emanuel of Liechtenstein cannot also be a Prince of Nassau now?
People routinely have multiple titles with one being considered the most important (sometimes in an order that is mysterious to outsiders) and therefore the one usually given but doesn’t necessarily preclude others not given.
He could be granted the title by grand ducal decree, but as an automatic thing, the current version of the house law says that the title descends in the male line only. Thus far, Grand Duke Henri has not issued a decree conferring the title on his nephew.
The full version of the decree (in German); an unofficial English translation.
I hope I’ve given ample time for answers, before posting a Nitpick in GQ, but …
Regarding OP’s question, the term “Prince” (let alone “prince”!) is exceedingly ambiguous.
Setting aside special terms like Crown Prince, Royal Prince, Prince of the Blood; even just Prince has been used variously:
(a) a generic word for ruler (especially, of a non-Republican country).
(b) A generic term for any noble or royal ranked Count/Earl/Graf or higher (or for, e.g. an Archbishop).
© a specific familial or courtesy title, e.g. for the son(s) of a prince (sense a or b). (Note that German Prinz is distinct from Fürst, also translated as ‘Prince.’ ‘Grand Duke’ was the dictated English style for Russia’s Imperial Princes.)
(d) the English translation of a specific European title (e.g. Prince (Fr.), Fürst (Germ.), князь/książę/etc. (Slavic), usually higher than Count and below a Duke.
(e) a very high sovereign or semi-sovereign noble rank, perhaps roughly equivalent to archduke.
(f) sometimes used for any male agnate of a Royal or Princely house; or for a male agnate nominated by the house’s head to bear such title.
A special case I’ll ask the Board’s Celticists about: IIUC, Wales had up to six royal rulers (‘Kings’) until unified under Llewellyn the Great. These rulers were just Arglwydd(?) but this is often rendered ‘King.’ (King of South Wales’ etc.) When Llewellyn unified the ‘kingdoms’ he took the title Tywysog, rendered as ‘Prince’ (‘Prince of all Wales’).
So I guess Russian Princes don’t count.Wikipedia lists one living pretender, and one that passed away as recently as 2016. As mentioned above, a Grand Duke is the equivalent of an English Prince, there are many other people who may be referred to with the title Prince, who may be in the royal line, but not at that level. The Wiki seems to say only the children and grandchildren of a Russian Emperor could hold the title.
The OP specifies only non-deposed houses. Pretenders do not count.
Yeah. I suppose that’s why I started my post by mentioning that.
Grand Duke George Mikhailovich of Russia would argue with you. He is a great-great-grandson of Tsar Alexander II, but claims the grand ducal title on the basis that his mother is the current head of the Russian Imperial House, his great-grandfather having claimed the throne as emperor in exile in the 1920s.
(Mind, a fair number of the rest of the surviving Romanovs would also argue against George Mikhailovich’s right to bear the title, including arguments over whether his grandfather’s marriage was equal, his great-grandfather’s marriage was in conformance with Orthodox canon law, etc., etc.)