An executive producer is a producer who is not involved in any technical aspects of the film making or music process, but who is still responsible for the overall production. Typically an executive producer handles business and legal issues. See also film producer, line producer. 
An executive producer of a motion picture is typically a producer who is sometimes involved with a property that has since been optioned into a film, but has no direct input into the creative process of the film itself. e.g. authors of optioned literary works.
In the production of a television show there may be many executive producers listed. Sometimes it may be a situation not unlike the one described above for motion pictures: someone with previous involvement with a particular work, a project's financier, or someone in control of the business aspect of production. Sometimes, this title is conferred upon a celebrity or notable creator who has lent their name to a project to boost its prestige or credibility, as a recognition of newly-acquired industry status, or as a perk to the show's main star or creative force.
However, under the unusual rules for establishing writing credits on television series (where writers are often credited as "producers"), the principal writer is almost always credited as an executive producer rather than the more descriptive title of "head writer."
In television an executive producer might have more power than any other credited crew member — this is the case with the show runner. Generally a show runner (still credited as an executive producer) is the creator of a series and/or an influential staff writer on the show. His or her role is to guide the overall creative progress of the show's story over the course of a season — basically, the de facto creative director of the show — and all creative decisions (from casting to script approval) go through them. Usually, while there may be many credited "producers" and "executive producers" (with varying responsibilities) on a television series, there are just one or two in the position of show runner.
For these reasons, it is not unusual for TV shows to have three sets of "Executive Producers:" Traditional EPs (Production Executives, Financiers, etc.), Head Writer(s), and Show runner(s).
In the music industry, the executive producer of an album is often in control of the business side of production, distribution, and promotion. This role can entail obtaining financing, allocating the budget, etc. At times, the executive producer may also provide artistic input such as which songs are placed in the final cut and the order in which the songs are placed. In this instance, the executive producer is usually someone who has had input in producing some of the tracks on the album. A particular executive producer's name attached to an album is sometimes used as a selling point to distributors.
The title "executive producer" is not well-defined in the video game industry. It may refer to an external producer, from the publisher, who works with the developer. Sometimes the title is used by the studio head of the developer who created the game.