Wargame
In 1956, Scruby organized the first miniature wargaming convention in America, which was attended by just fourteen people. From 1957 to 1962, he self-published the world's first wargaming magazine, titled The War Game Digest, through which wargamers could publish their rules and share game reports. It had less than two hundred subscribers, but it did establish a steadily growing community.
Around the same time in the United Kingdom, Donald Featherstone began writing an influential series of books on wargaming, which represented the first mainstream published contribution to wargaming since Little Wars. Titles included : War Games (1962), Advanced Wargames, Solo Wargaming, Wargame Campaigns, Battles with Model Tanks, Skirmish Wargaming. Such was the popularity of such titles that other authors were able to have published wargaming titles. This output of published wargaming titles from British authors coupled with the emergence at the same time of several manufacturers providing suitable wargame miniatures (e.g. Miniature Figurines, Hinchliffe, Peter Laing, Garrisson, Skytrex, Davco, Heroic & Ros) was responsible for the huge upsurge of popularity of the hobby in the late 1960s and into the 1970s.
In 1956, Tony Bath published what was the first ruleset for a miniature wargame set in the medieval period. These rules were a major inspiration for Gary Gygax's Chainmail (1971), which in turn became the basis for the roleplaying game Dungeons & Dragons.
From 1983 to 2015, Games Workshop produced what was the first miniature wargame designed to be used with proprietary models: Warhammer Fantasy. Earlier miniature wargames were designed to be played using generic models that could be bought from any manufacturer, but Warhammer Fantasy's setting featured original characters with distinctive visual designs, and their models were produced exclusively by Games Workshop.

Board wargaming (1954–present): The first successful commercial board wargame was Tactics (1954) by an American named Charles S. Roberts. What distinguished this wargame from previous ones is that it was mass-produced and all the necessary materials for play were bundled together in a box. Previous wargames were often just a rulebook and required players to obtain the other materials themselves. The game was played on a pre-fabricated board with a fixed layout, which is why it was called a board game.
Roberts later founded the Avalon Hill Game Company, the first firm that specialized in commercial wargames. In 1958, Avalon Hill released Gettysburg, which was a retooling of the rules of Tactics, and was based on the historical Battle of Gettysburg. Gettysburg became the most widely-played wargame yet.
Board wargames were more popular than miniature wargames. One reason was that assembling a playset for miniature wargaming was expensive, time-consuming, and require artisanal skill. Another reason was that board wargames could be played by correspondence. Board wargames were usually grid-based, or else designed in some way that moves could be explained in writing in simple terms. This was not possible with the free-form nature of miniature wargames.

Notable people: 

Wargaming as a hobby: Georg von Reisswitz, who with his father invented Kriegsspiel.
H.G. Wells – Pioneer in miniature wargaming, author of Little Wars. His usual companion in wargames was Jerome K. Jerome (of Three Men in a Boat fame).
Jack Scruby – After H.G. Wells, he did the most to make miniature wargaming a respectable hobby. He also popularized miniatures wargaming with a cheaper production process for miniature figures, publishing the first miniature wargaming magazine, the War Game Digest, and community building.
Don Featherstone – Known in the UK as the "co-father" of modern miniature wargaming.
Charles S. Roberts – Known as the "Father of modern board wargaming", designed the first modern wargame, as well as the company most identified with modern wargames (Avalon Hill).
Phil Barker – Co-founder of (Wargames Research Group), co writer of WRG Ancients in 1969 and of DBA the innovative 1990 ruleset.

Designers/developers: Richard Berg – Designer of Terrible Swift Sword, and worked at SPI.
Larry Bond – Designer of Harpoon, and best selling author
Frank Chadwick – A co-founder of Game Designers Workshop (along with Loren Wiseman, Marc Miller, and Rich Banner), one of the first major competitors to Avalon Hill, and himself a prolific wargame designer and innovator.
Jim Dunnigan – considered "The Dean of Modern Wargaming", founder of SPI and the most prolific print wargame designer in history. His designs included many firsts in wargaming, including the first tactical wargames.
Charles Grant – Author of The Wargame.
E. Gary Gygax – Designer of several miniatures and board wargames who went on to co-create (with Dave Arneson) and publish Dungeons & Dragons.
Larry Harris – Designer of Axis and Allies, Conquest of the Empire, and other games in the Axis and Allies Series.
Bruce Quarrie – wrote rule sets for Napoleonic and World War II wargames and also on military history.
John Hill – Designer of Squad Leader, Johnny Reb, and other well-received designs.
Redmond Simonsen – Co-founder of SPI and introduced many advanced graphics design elements to wargame designs.

Notable players: Peter Cushing – Actor
Curt Schilling – Former baseball player and commentator

Notable examples: 

Board: While a comprehensive list will show the variety of titles, the following games are notable for the reasons indicated:

Diplomacy – (1954) a classic multi-player game from the "golden age" of wargames in which strategy is exercised off the game board as well as on it.
Tactics II (Avalon Hill, 1958) – the wargame that launched Avalon Hill.
Risk (Parker Brothers, 1959) – Widely accepted as the first mainstream wargame.
Gettysburg (Avalon Hill, 1958) – the first modern era wargame intended to model an actual historical event.
Tactical Game 3 (Strategy & Tactics Magazine game, 1969); re-released as PanzerBlitz by Avalon Hill in 1970. The very first tactical wargame. The game pioneered the use of "geomorphic mapboards" and PanzerBlitz was a game system rather than just a game in that forces could be used to depict any number of actual tactical situations rather than one specific scenario. Pioneered several ground-breaking features, such as use of various types of weapons fire to reflect battlefield conditions. Also created new level of realism in reflecting tactical armored vehicles.
Quebec 1759 (Columbia Games, 1972) – The first wargame to use wooden blocks with labels to provide a fog of war and four possible steps of strength.
Sniper! (SPI, 1973) – along with Patrol, the first Man to Man wargames where game pieces depicted a single soldier. An adaptation of Sniper! also became one of the first multi-player computer wargames.
Wooden Ships and Iron Men (Battleline Publications, 1974 Avalon Hill, 1976) – the definitive game of Age of Sail warfare for many years.
Rise and Decline of the Third Reich (Avalon Hill, 1974) – The first serious attempt to model World War II in Europe in its entirety, including (in a limited way) the economic and industrial production of the nations involved. It has seen numerous versions and editions, and is currently available as John Prados' Third Reich from Avalanche Press, and as a far more complex descendant game, A World At War, published by GMT Games.
La Bataille de la Moskowa (Martial Enterprises, 1974) Later republished by Games Designers Workshop and Clash of Arms. With 4 maps and 1000+ counters, it is credited with being the first "monster" wargame (by famed designer Richard Berg.)
SPQR (GMT Games, 1992)
Squad Leader (Avalon Hill, 1977) and Advanced Squad Leader (1985) have become the most prolific series of wargames, including 3 add-on modules for the former, and 12 for the latter, with additional Historical modules and Deluxe modules also having been released. ASL also sets the record for sheer volume of playing components, with thousands of official counters and 60+ "geomorphic mapboards" not counting Deluxe and Historical maps.
Star Fleet Battles – (Task Force Games, 1978) one of the older still actively played and published wargames today; based on Star Trek, it is arguably the most successful tactical space combat system that does not rely on miniatures (published by Amarillo Design Bureau).
Storm Over Arnhem (Avalon Hill, 1981) – pioneered the use of "point to point" or "area movement" in tactical wargames.
Axis and Allies – (Nova Games, 1981) the most successful of Milton Bradley's (1984) 'GameMaster' line in an attempt to bring wargaming into the mainstream by appealing to non-wargamers through simplicity and attractive components.