Here in Mexico, the slang phrase qué padre (or variations such as muy padre, etc) are quite common, with the meaning "how cool".
Is this just Mexican slang, or do other regions use the same phrase?
The Academia Mexicana de la Lengua lists it in the Diccionario breve de mexicanismos, which would tend to support the anecdotal evidence that everyone has given so far (and that I would add to - I heard it a lot in Mexico, but I've only heard it from Mexicans elsewhere that I can recall).
I've heard that padre is predominantly Mexican slang.
As far as I know, it's mostly mexican, and probably used in zones near Mexico.
There is no universal translation for "how cool", although I've heard "está de pelos" in neutral Spanish translations, which means you can use that and be understood in all Latin America, although it will sound artificial.
Here along the Tex/Mex border, "Que Padre" is used by women who see man who they are and want to impress; when the man says something suggestive to a woman he hopes to impress, if receptive, she will respond and the with "que padre" indicating she is on the same page as the man and the new relationship has the potential to advance from there. It is also meant to encourage the man to pursue her further. Here in the Rio Grande Valley, it is all about reading the slang in the appropriate manner and advancing to the next stage. We have many colloquial sayings which are indigenous mainly to the lower Rio Grande Valley and they are a reflection of our particular way of life on the Tex/Mex border. We often refer to the language here as "Splanglish" and many times it is a mixture of Mexican and English. It is a way of life like no other.
Regarding the use along the Tex/Mex border, that seems a bit of a stretch. It's not meant to be used to impress a woman in a courting relationship.
The other reference above to "Está de pelos" is considered somewhat vulgar as well, as shouldn't be used in polite company.
I'm married to a Mexican woman who is from just south of the US/Mexico border, however, the use of the idiom "Qué padre!" can be evidenced throughout Mexico in the larger cities such as Tijuana, Guadalajara, and D.F. (cities from which I also have many friends). Simply translated, it does mean "how cool," or "how nice." The word "Qué" being the modifier for "how" (i.e., "very") and "padre" meaning "cool" or "neat" or "nice." Literally translated it would be "How father" or "What father".
In reference to the "courting relationship" example that one person provided above, a response of "Qué padre!" by a woman is the same as the woman saying in English, "that sounds so neat/cool," not as a function to advance the relationship, but to provide a positive "slang" response that may be generally acceptable in mixed company instead of a simple "Sí" ("Yes"), or "Qué bueno" ("How nice/good").
It interesting to note that the English idiom "How cool!" meaning
The diccionario de americanismos has an entry on padre:
1. adj. Mx. Bonito, bueno, estupendo. pop + cult → espon.
2. adv. Mx. Muy bien. pop + cult → espon.
3. adj. Gu. Muy grande, impresionante.
So from what we see, padre meaning cool is just reported to be used in Mexico. From this we can assume that qué padre meaning how cool is only prevalent in that country.
It is also interesting to see how many different, regional meanings this word in expressions:
a. ǁ ~ sin cabeza. m. Ho, Ni, CR. Personaje mítico en forma de sacerdote sin cabeza, que se aparece a los vagos y borrachos.
a. ǁ el ~ de las mentiras. loc. sust. Ho, Ni, Bo. El diablo.
b. ǁ ~ Gatica. loc. sust. Ch. Persona que no practica lo que recomienda. pop + cult → espon ^ fest.
a. ǁ no se oye, ~. fr. prov. Gu, Ho, Ni, Bo, Ch. Indica que hay alguien, incluido el propio hablante, que finge no oír o se niega a escuchar lo que se está diciendo porque no le conviene o no le interesa.