Note: I don't actually have a favorite game-- this is the first in a planned series of my favorite game of each genre
Master of Magic is a fantastic strategy game developed by Simtex (The same developer as Master of Orion) in 1995. Though I played it when it first came out, I was way too young to properly appreciate how great the game really was.
MoM plays a lot like the original Civ spiced up with tactics-style battles. After picking a wizard and race, you start off with a single city in the middle of unexplored teritory. You pick which building or unit you'd like the city to create, and then pick a spell to research. You also start with two units for scouting or defense.
There's two types of currency in the game: Mana and gold. They're convertible in a 2:1 ratio, so in a pinch you can liquidate your coffers to cast a mana-expensive spell. Around the map, you'll eventually come across Mana Nodes. These tend to be guarded by powerful monsters or droves of weaker ones, though the reward for killing them is very important. Once the Node has been cleared of monsters, you can move a special unit onto it to 'meld' with the Node, which then starts generating large amounts of mana for you.
You'll also find a few other event tiles littered around the map. Various ruins, temples and caves can be found, with matched guardians. Prizes for looting them generally tend to be gold and mana, though you can find artifacts as well.
To use artifacts, you'll need heroes. Heroes will occasionally offer to join you, with the calibur of hero largely dependant on your Fame stat. Heroes have a few equipment slots for artifacts, and can act as normal units in battle. Heroes become very important due to their good stat growth, and abilities. Many heroes (and a good amount of normal units) have special abilities that can let them do things like ignore damage from specific sources, use ranged attacks, or reanimate enemy units as various undead creatures. Obviously, balance can be an issues with some higher-level heroes.
My favorite part of this game, however, is the ability to customize your wizard in the begining of the game. You can chose from a list of pre-rolled wizards, or create your own. The game will prompt you to chose a portrait for your wizard, and then will bring up a list of traits and proficiencies in the 5 realms of magic your wizard can have.
You start out with 11 'picks', which you can spend on traits and 'books' of magic. The more books you take in a school of magic, the more spells of that school you'll start the game with, and the more spells you can eventually research.
Picks can also be used for traits, which change certain rules for your character. "Myrran" starts your character off on the second plane of existence in MoM, and generally you're one of the only players there. The various magic masteries let you collect mana from nodes faster. Some of the traits cost more then one pick, depending on how powerful it is.
Battles are played out on an isometric grid. You move your whole army in a turn, unit by unit, and then your opponent gets to do the same. You (or one of your heroes, if they have the ability to do so) can throw spells in battle, though you're limited on how much mana you can spend in one battle by your "skill" stat.
The game has two victory conditions. The first one is simply to wipe every other player off the map. Honestly, this is the victory I tend to get most often. The other condition is to research and cast the Spell of Mastery. However, the spell takes forever to research and longer to cast, and the AI has a nasty tendency to instantly declare war on you when you begin casting it.
All-in-all, Master of Magic is my favorite strategy game. It left a legacy in the realm of strategy games (Many of Master of Orion II's features were ripped directly from MoM), and Stardock has talked about making a spiritual sequel to the game.