Ben Grimm, no doubt, calls his “The Thing.”
Frank Castle refers to it as “The Punisher.”
Ted Knight likes to style his as a “cosmic rod.”
Your turn.
Well, Clark Kent has “the Man of Steel.”
No need for dick pills there.
Spiderman has his palpal organs! Er … spinnaret? I guess that’s not what your looking for. How about his “web swinger”?
“They call me Captain Hammer, but these… these aren’t the Hammer.”
Spiderman has a web shooter.
Captain Marvel has his Little Billy.
Nightwing has his night-thing.
Robin has his Boy Wonder.
How about for the ladies?
Powergirl has powergirls.
Doctor Manhattan has Big Blue.
The Comedian’s is Mr. Happy.
Cyclops has his One-Eyed Power Beam.
ShadowCat has her…nah, too obvious.
Magneto has his Monopole.
Martian Manhunter has the Martian Man-parts.
Blue Beetle has his blue… wait a minute…
It’s called the web-slinger. I think it fits perfectly. 
Whereas Superman has “Red Kryptonite”.
Reed Richards of course has Mr. Fantastic.
Doctor Strange has his Dread Dormammu.
Well, obviously I’m not very good at this. I actually looked up the name of a male spider’s parts. Anyway, I know he has a web-slinger but I thought his spidermember would be more of a swinger.
Anyway, if you like this sort of thing there was a hilarious thread about “Thing’s thing” posted here a while ago. Maybe someone would like to brave the search?
Feric Jaggar affectionately calls his “The Great Truncheon of Stag Held.”
Ted Sallis, IIRC, had a Giant Size Man-Thing.
I believe Green Arrow has the long sharp pointy thing,
I initially thought this was a “Cosmic Cow” reference.
“Meanwhile, at the Hall of Justice…”
Apache Chief has the “Li’l Chief”
Calcium Man has “the Milkbone”
Poison Ivy has a “lily” (or briar patch, if you’re mean)
Catwoman has a … well, you know (same thing as ShadowCat)
Spider-man actually can’t have sex, though. If he did, he would immediately die, his genitalia lodged inside the woman so that no other males have a chance to impregnate her. (cite).
Scott Free flatters his as “Mr. Miracle.”
(Of course, if we assume that Barda really is Big…)
Wonder Woman has her Paradise Island.
You’ve been with Spider-man?!!