Shonen Jump

Shonen Jump was an English-language Shonen manga anthology magazine that was published by Viz Media in the US from January 2003 to March 2012, based on Weekly Shonen Jump, a Japanese magazine which began in July 1968. It mainly carried translations of manga that first appeared in Weekly Shonen Jump. The magazine introduced many Americans to some great series, such as Naruto and One Piece. According to The Other Wiki, it featured a total of twelve series in its first six years, previews of many others that Viz publishes, and articles on Japanese culture and language. In addition, every issue included anime, manga, and video game reviews as well as tips for various card games related to manga series, and several times included promotional cards with an issue (some of which were Promotional Powerless Pieces of Garbage).

In early 2012 Viz closed the doors on Shonen Jump to replace it with Weekly Shonen Jump Alpha, a digital version of the magazine they had announced the prior year. WSJA contained their six most popular manga alongside bonus material such as sketches and interviews with the Japanese side of the industry. Issues cost $1 per issue or $26 for a year's subscription. It ceased publication in December 2018.

The original Japanese magazine is practically synonymous with works that focus primarily on fighting and action; shonen jump is often considered to be its own subcategory of shonen anime and manga.

A Shoujo-oriented sister-magazine to the Viz Shonen Jump called Shojo Beat! came out in the early 2000's, but sadly it didn't make as much money as the publishers hoped, and in 2008, the magazine was discontinued. The Japanese Weekly Shonen Jump currently has a number of sister magazines, including the Shonen Jump Square (a replacement for the discontinued Monthly Shonen Jump), and the Seinen Weekly Young Jump (more sex and violence), Super Jump (drama/action-oriented), Ultra Jump (fantasy/SF oriented) and Business Jump (aimed at the Salaryman audience).

Many of these series are featured in Jump Super Stars.

Series run in Shonen Jump

Series run in Jump Square

Blue Exorcist (ongoing)
Claymore (ongoing)
D.Gray-man (ongoing)
Dragonaut: The Resonance
Embalming (ongoing)
Genkaku Picasso
Karakuridouji Ultimo (ongoing)
Kure-nai (ongoing)
Kurohime
Mayoi Neko Overrun
Papa no Iukoto o Kikinasai (ongoing)
The Prince of Tennis (ongoing)
Rosario + Vampire (ongoing)
Sengoku Basara 3: Roar of Dragon
Shiki
Tales of Innocence
Tegami Bachi (ongoing)
To Love Ru Darkness (ongoing)
Yoku Wakaru Gendai Mahou

Series run in Monthly Shonen Jump, but not Jump Square

Series run in Weekly Young Jump

B Gata H Kei
Elfen Lied
Gantz (ongoing)
Liar Game (ongoing)
Rozen Maiden (ongoing)

Series run in Super Jump

Series run in Ultra Jump

Akikan
Aqua Knight
Bastard!! (ongoing)
Gingitsune (ongoing)
Gunnm: Last Order
Hayate × Blade (ongoing)
NEEDLESS (ongoing)
Ninku
Outlaw Star
Read or Die
Steel Ball Run
Tenjho Tenge

Series run in Business Jump

This magazine contains examples of:

Bishonen Jump Syndrome: The Trope Namer.
Doorstopper: Consistently tops out every issue at about 350 pages, and is one of the few non-fashion oriented magazines to do so. Its Japanese counterpart frequently hits 500 pages, and comes out every week.
Dueling Shows: Naruto vs One Piece, Fairy Tail vs One Piece, Toriko vs One Piece.
Honorifics: Even outside the manga themselves. The pages that teach fans about the Japanese Language sometimes have explanations of honorifics as the main topic or as part of some larger lesson.
Manga Effects: Duh, considering its a manga anthology. Also occasionally used in the articles and reviews.
Promotional Powerless Pieces of Garbage: Some of the Trading Card Game cards included with some issues.
Puzzles: Most issues have some kind of puzzle related to one of the featured series.

And of course, all the various tropes presented in the series themselves.