Me juego el cuello a que...

[poli]

translates: I'd bet my neck on it that...

Is this as common as it is in English?

[Tomisimo]

As a subjective opinion based on my experience, I'd say it's not as common as in American English, but it probably depends a lot on the speaker and where they're from.

[Perikles]

translates: I'd bet my neck on it that...I've never consciously heard that expression, I would always say I'd bet my life ...

[poli]

Of course I've heard I'd be my life
also: my ass (vulgarly)

: my eye teeth

similarly: you bet (meaning yes mostly in the Midwest United States)
you bet your boots.

[JPablo]

"Me juego el cuello" doesn't sound uncommon in Spanish to me. Probably is getting a bit dated, but I believe any Spanish speaker will get it.
Oxford bilingual gives,
me juego el cuello a que no lo hace = I bet you anything you like he doesn’t do it / you can bet your life he won’t do it.

With "neck" in English I heard, (again Oxford)
to risk one’s neck = jugarse/arriesgar el pellejo; to stick one’s neck out = aventurarse, arriesgarse.

[sosia]

common for me. usuall in sports or tv, where "changing heads" is more usuall... :D
-El entrenador se jugó el cuello al sacar del campo a Cristiano Roanaldo...
-La cadena se jugó el cuello al programar la nueva serie...

saludos :D

[ROBINDESBOIS]

In Spain we bet the neck instead of the life.

[sosia]

agree with robin
"se jugó la vida"/"bet the life" is spanish only in his literal meaning:
-"El bombero se jugó la vida para rescatar a la niña del incendio"
but not as idiom
-"El directivo se jugó la vida apostando por la recuperación de la empresa"
This sentence means the manager was sick and continued working....

saludos :D