www.alphadictionary.com

No, this word, which is hardly current (only three of the 922 dictionaries to which alphadictionary.com provides access list an entry), and which one is most likely to hear on an obstetric/neonatal ward, does not mean what you think it does ! But inspired by wordsmith's A.Word.A.Day, I thought I'd suggest it as GWotD, despite the possibilities for misunderstanding....

Henri

vagitus (vuh-JI-tuhs) noun

The cry of a newborn.

[From Latin vagire (to wail).]

Yes, I thought of what you thought I had thought of, but then I remembered this Portuguese word vagido, which, besides having the sense you pointed to, also means lamentation, whining, complaint, in Portuguese (2nd definition).

Brazilian dude

Garzanti provides a definition of the Italian verb «vagire» similar to the one for the English noun above, but interestingly enough a second definition as well, which is metaphorical and refers not to the wailing but to the time at which it takes place :

v. intr. [io vagisco, tu vagisci ecc. ; aus. avere]
1 piangere, detto di neonati
2 (fig. lett.) essere agli inizi, ai primordi, detto di un'arte, una civiltà e sim.

Henri

I remember reading a book that suggested Vaticanus is related to vagitus. "Va" (/wa:/) seems to be a cross cultural onomatopoeia for vagitus voice.

but interestingly enough a second definition as well, which is metaphorical and refers not to the wailing but to the time at which it takes place :

La ringrazio tanto, Signor Henri, non n'ero proprio conscio.

Brazilian dude

I love words that wakeup the dirty-minded only to turn out to be positively antiseptic. There is little in dictionaries (other than medical dictionaries) on the word, so if you know of any cognates in other languages, like the Portuguese and Italian ones already mentioned, I would be obliged.

but interestingly enough a second definition as well, which is metaphorical and refers not to the wailing but to the time at which it takes place :

La ringrazio tanto, Signor Henri, non n'ero proprio conscio.

Brazilian dude

"Wasn't Tanto the Lone Ranger's Faithful Indian Companion?"

"Ah, no, that was Tonto, Kemosabe."

"Oh."

Spanish: vagido
s.m. Voz o llanto característicos del recién nacido
ETIMOLOGÍA: Del latín vagitus, y este de vagire (gritar, lanzar un vagido).
ORTOGRAFÍA: Dist. de vahído.
http://clave.librosvivos.net/

French: Vagir - Pousser de faibles cris. Vagissant, ante - Qui vagit. Vagissement n.m. - Cri de l'enfant nouveau-né; Cri plaintif et faible (de quelques animaux)
Le Robert Micro Poche

Catalan: vagit
[s. XX; del ll. vagitus 'crit, crit de dolor']
m Gemec, plor, de l'infant acabat de néixer.
http://www.grec.net/cgibin/lexicx.pgm?GECART=0140144

Brazilian dude