Classic Empire
Back in the 1980's, Empire was award winning Wargame of the Century and one of the first computer wargames ever created. Released for a number of different computers by Interstel Corporation, game got a number of sequels which are still played today. Classic Empire is the free version for modern PCs from the original creator, Walter Bright. Game is very minimalistic, but still the same world conquest city by city with a small selection of different units. Careful with movement! If you move ground force army to water by mistake, you lose it! If you move ship/fleet to land by mistake, you lose it! If you try to load an Army onto Transport already in full capacity, you lose that Army! Simple but fun, and much recommended to newcomers to war strategy game genre.
Empire Deluxe Combined Edition
There has been a number of commercial releases of Empire. This is the newest and most advanced. Game has lots of options, buttons, and editors, but don't let that scare you: by its heart, EDCE is still the same world conquest city by city as its predecessors. You can start the game with the default settings, and it'll be even easier than Classic Empire: whole map is revealed, enemy units and their moves are visible to player, map is of modest size, and there is literally only handful of different units available for production. Crank up all the settings to advanced and tick the checkboxes, and game has long list of units that include satellites and long range nuclear missiles along with supply to worry about. Variety of buttons come in handy to set up patrol routes for aircraft (fly around the city, land to the city to refuel, repeat), automatically move new units from inland city to port city, and more. Gradual increase of depth and complexity and a number of scenarios and mods available for download make this an excellent starting game for newcomer.
Field of Strategy II
Grand tactical (is that a term?) scale square grid based wargame which covers great many historical eras. Game play isn't too hard: click on a unit, available squares are highlighted, click on where you want unit to move, and it goes there. Combat is automated. Important things are maneuvering and unit positioning: enemy is crushed with concentrated attack of multiple units from different directions. Therefore flanking plays a crucial roles, as does proper use of terrain. Napoleon's cannons won't shoot through friendly units unless they (cannons) are on the higher ground.
Multiplayer SHOULD work directly between players, but I didn't get it to work; other player's firewall is to blame? But developer has a dedicated multiplayer server. When all the players (can be more than 2) are in attendance, game can be played in real time (still turn-based) between the players. Alternately players can play their turns when they feel like, and saves stay in the server. Log in to check is it your turn, play your turn, turn the game off, and log in the next day (or the next week) to check on is it your turn again. This is BRILLIANT!
Battle for Wesnoth
Now THIS is an excellent example of open source game. Wargames in general aren't winners of a beauty contest, but Battle for Wesnoth don't need to be ashamed of its looks. Game is fantasy strategy game. I haven't played Fantasy General but I guess it is good example for comparison. Available sides include humans, elves, orcs... standard fantasy stuff. Variety comes to play in form of traits. Each new unit gets two traits which are assigned randomly. Traits may increase unit's attack damage, speed, hit points etc. When unit fights, it gets experience. When unit has enough experience, it can be promoted to a more effective unit.
Player(s) can spend gold to get new units. Gold is get from villages in form of tax. In addition villages and base (castle/fortress/camp) itself offers defense bonus and heal units which are located in them. Large number of units require gold for upkeep. "Army marches on its stomach" you know. In single player scenarios there are a number of objectives to be completed. Multiplayer seems to be traditional 'kill them all'.
But what really hits the eye is a very long list of available languages. I was startled when my native language was on by default and all I could do was stare at the screen and think "WTF!!?" Finnish translation isn't too bad, but there are enough errors and gaps (English mixed together with Finnish) for me to prefer English (UK version).
Sunrider: Mask of Arcadius
Tactical space combat from Japan. And because it's from Japan, fighters got replaced with mecha. At least game is turn-based on hex grid. Otherwise game play isn't anything too convoluted: armed carrier and accompanying mecha move and shoot within a limited number of points per turn. Few things stand out. Missiles have range and power, but numbers are very limited and can be shot down, possibly by multiple units along the way. Some units carry energy shields which can be used to cover other friendly units to reduce damage, and multiple shields stack up. Player's mechas aren't identical rank & file carbon copies, but each is unique and irreplaceable (when HP goes 0, they retreat). Some of the mecha are equipped for electronic warfare to temporarily shutdown entire enemy unit, or (with smaller point cost) some of its systems (shield or flak). Unit damage is seemingly only hit points and weapons or other stuff don't break down. Scenarios aren't necessarily "kill them all", but usually have objectives, like destroy the base/leader. In addition reinforcements can appear on either side. Attacks are animated (for every attack, maybe it can be turned off?), possibly along with a character portrait and 1-liner from voice actress. Between scenarios equipment can be upgraded and weapons (like missiles) bought. Game has also a visual novel element, where player can go around the ship by clicking on hot spots on the floor plan to chat with the crew.
Available on:
Good Old Games
Steam
) I recommend Jagged Alliance series.