Are there any living people with a plausible claim to be Holy Roman Emperor? (BTW-It was neither Holy, nor Roman, nor an Empire) 
It doesn’t seem likely. The Empire was dissolved in 1806 by Francis II. At that point, the Imperial title wasn’t hereditary, in theory. In practice, in the latter days of the HRE, it almost always went to a Habsburg, but that wasn’t necessarily a foregone conclusion. With no tradition of de jure hereditary ascension, the Imperial crown as a concept ceased to be.
Thanks jayjay! I asked the OP before wikiing and seeing that it was an elected monarch.
Like on Naboo?
I went to Wikipedia.
No, he’s saying that, in the Star Wars prequel trilogy, Naboo had an elected monarchy as well.
Once again I got whooshed!
If you assume that the Hapsburg heirs would continue to have been elected up until the present day, then I give you your emperor.
Following the epic 88-year reign of his father (who was probably the smartest Habsburg in 300 years).
Of course none of the above are/were real Habsburgs :D.
The last male Habsburg, the HRE Charles VI, croaked in 1740 ( to be briefly succeeded by the non-Habsburg Wittelsbach emperor, Charles VII ). The later descendants are all through the female line, the male-line dynasty changed to the House of Lorraine who is a moment of propagandistic realpolitik took the new dynastic name of Habsburg-Lorraine to associate themselves with the more prestigious imperial house. Fair enough, really - the last male-line Habsburg period, Charles VI’s daughter Maria Theresa, was de facto the real ruler in her day. Her husband, the eventual HRE Francis I of Lorraine, kinda functioned as more as her figurehead and personal secretary.