Hm...I wouldn't say "normal," but I might not go so far as to say "trashy."
I mean, it's got ancient roots...then again, it was the title of a high-profile action movie featuring a scantily-clad, sai-weilding title character (played by Jennifer Garner) not long ago. Plus, there's always the association with electricity.
If that's the continuum (normal at one end, trashy on the other) I would personally put it more toward the "trashy" end, but not all the way over. Others may disagree, though.
I agree with Nancy. Also, another association (even though a "surname") is Carmen Elektra.
I totally forgot about Carmen -- good call. That's another not-so-classy association that might turn some people off.
What's in a name? It depends on who you are, and your frame of reference...
First off, this is a perfectly respectable ancient name. Elektra is a daughter of Atlas and with Zeus, mother of Dardanus, legendary founder of Troy.
What is your social milieu, ethnicity? Are you Greek? If your friends first frame of reference regarding the name "Elektra" are Prince prot�g�s and comic book characters, perhaps you'd best forget this name. If you and/or your friends are classical scholars, artists, eccentric or intellectual types, go for it.
I'd venture to guess that the latter is probably not true of your coterie, because for want of a better expression, the name "Elektra" could be qualified as "if you have to ask, you can't afford it." This is a non-conformist name that requires a strong personality to carry it off... An Elektra doesn't need anyone's advice, do you know what I mean?
I know all of this because my own five-year-old daughter is named Elektra. The name is perfectly her, and she carries it with aplomb. We live in Europe, where people are far more familiar with the Classics than in the US... and people are happy to hear an authentic and original name, in a world of Emilies, L�as, Thibauds and Quentins (in my neck of the woods, anyway)...