When dubbing foreign movies or TV shows in Spanish for an international audience, what dialect or variety of Spanish is typically used? Does it vary, or is there a particular variant that's considered most "neutral" or "standard"?
I would say Argentina, Spain and Mexico -in that order- are the 3 countries where most of the movies and TV shows are dubbed today. Dubbing companies from other countries are entering the business now (Venezuela, Colombia) but when I was younger, most, if not all of the of the cartoons and TV shows where dubbed in Argentina while the movies where dubbed in Spain or simply not dubbed at all. You had to read the closed captions.
As far as using a neutral accent, I suppose it depends more on how good the company doing the dubbing is, but Argentinian companies are the best in my opinion. They rarely use regionalisms (ie. they dub
Mexican and Spanish companies, at least on my experience, are not so good and
Disclaimer: This is totally based on my own experience and I did not use any other reference to support my claims.
In Spain, films and other shows are dubbed in "neutral" Castillian, i.e. with no evident regional accent. As Javi says in a comment, that's mostly what's used in the center and North of Spain.
Sometimes, when the film has a character whose accent in the original is important to the plot, they use a "not-so-neutral" accent, e.g. for Scottish people in the USA, or some Mid-Western with strong accent in NYC.
And when there's a character from Latin America, even if he speaks in English in the film, they dub him in some Latin American Spanish (probably, because the accent was identifiable in the original).
Usually, what's in Spanish in the original is left as is, but there are notable exceptions, where they dub it to show that the character was not speaking his own language (e.g. in Terminator 2, "hasta la vista, baby" was dubbed as "sayonara, baby").
Sometimes, even films where the characters speak different languages and that fact is central to the plot, e.g Vicky, Cristina, Barcelona, are dubbed to all-Spanish, [rant] and they all end up looking like idiots, because they don't understand each other even if they are speaking the same language [/end of rant]. A notable exception to this is Spanglish which we saw here in its original version, with subtitles for the parts in English.
Regarding cartoons and animation films, many used to be dubbed in America (Mexico, I guess). In fact, all Disney Classics up to The Little Mermaid were dubbed in America. It was the same with Warner Bros., Hannah-Barbera, etc. The new reissues of those films are being redubbed into Castillian, which curiously enough, makes them sound a bit weird now, after having seen them always in American Spanish.
And that's more or less how things are in Spain regarding dubbing. I can't speak about the Americas, since I don't know anything about their media markets.