Well, the hobby died out; the rules for these games were too complicated to have a broad market; the market for these wargames dried up in the early 1980s when home computer video games started entering the scene and Dungeons and Dragons took over. The only game with rules simple enough to have general appeal was Axis and Allies, which was published by the Milton Bradley Company in the mid-1980s; the game is still around and is published by what little is left of Avalon Hill.
However, the hobby still lives because there are a number of high-quality, free computer games out there that handle the complicated rules for you, have fog of war—the ability to not always see what your opponent is doing—something that never was possible with those old board games, the ability to easily save games to load at a later time, random map and scenario generators, and play-by-email support.
In my experience, the Windows-only games that aren’t open-source have the most compelling game play (but see postscript below). My favorite game right now is People’s Tactics which is the free “teaser” version of the far more advanced and flexible Advanced Tactics. The game comes with a number of scenarios, has a random map/scenario generator, and even allows you to make your own scenarios with control over pretty much any game parameter.
The rules are simple enough that I was able to go through the tutorial in about 30 minutes. Typical of turn-based strategy games, gameplay is slow: it takes three or four hours to finish a small randomly generated 23x23 map, and maps can be up to 100x100 in size. The game is nice because it runs in a window instead of using full-screen mode, allowing me to easily check my email and perform other tasks on my computer while playing the game.
The game offers a lot of play and, when I get a job with a living wage again, I will pay the $40-$50 to support the author and get the more extensive Advanced Tactics.
Another series of hex-based wargames that are free are games in the Steel Panthers line. “Steel Panthers: World at War” is a tactical-level hex-based turn based simulation of World War II, complete with random terrain and random scenario generators. There is a thriving community with hundreds of user-created mods at spwaw.com. Another related free game is “Steel Panthers: World War II”. I have not had a chance to learn these games yet to give a full review, but SP:WaW looks very popular based on the huge number of scenarios and mods available for it.
To download People’s tactics, go to this webpage and look for “Download People’s Tactics” on the left (scroll the page down) or the box with the label “People’s Tactics” on the right (again, you will need to scroll the page down):
http://www.advancedtactics.org
Edit: Thinking about it some more, I neglected to remember two compelling open-source turn-based strategy games: Battle for Wesnoth which I enjoy greatly, and, while I haven't played it, Eight Kingdoms looks compelling.