Sword of Aragon. This game is one of my favorite games of all time. Fair warning, this game came out in '89, so the graphics are pretty amazing. You are the son of the slain ruler of Aladda, and your quest is to reunite the kingdoms of Aragon. You'll start the game by choosing a Warrior, Knight, Ranger, Priest, or Mage. This guy is you, and you'll see him in battle with a little flag that he carries around.
You'll want to recruit other heroes and form regular army units in order to defend against attacks on your city as well as capturing other cities or vassalizing them. In battle, your units and heroes will gain experience and level up, unlocking new equipment and spells (heroes only). You can have lightly armored "sword and board" infantry, or you can give them a huge, two-handed claymore and platemail. Similarly, archers can have anything from crossbows to compound bows, which affect what melee weapons they can carry in case you get charged by enemy calvary.
There are plenty of events that happen, some of which require you to choose an action such as sparing the life of an accused killer or seeing him executed. Girls are kidnapped by a minotaur. A dragon blocks your advance on a goblin stronghold. Do you kill these beasts or cower in fear? Your cities require your attention as well. Build up your agricultural, logging, mining, manufacturing, and commercial districts. Build more houses and bigger fortifications. Wait for the local populace to get in line to be recruited or forcibly conscript them into your army.
I've played hundreds of hours of Sword of Aragon and continue to get a run in every few months. The game's graphics are nothing to write home about, but the gameplay is fantastic. Best of all, it's free since it's abandonware. Here's a link to download it, if you're interested.
Other notable mentions off the top of my head include Dune (point and click), Dune II (real-time strategy), and X-COM: UFO Defense (turn-based tactics). I'd be happy to give you a run down on any of these games (and possibly others) as well.