Without this game, and the previous Empire, we would not have RTS games.
This is pretty much as simple as old-school war games get. Your goal is to conquer your opponents by capturing all their production centres on the map (i.e. cities). Only the army, a land unit, may capture them - all the other units are basically just strategy support. Each city you own can be made to produce any unit after a set number of turns (varying for each unit). Extremely simple, extremely addictive.
Empire Deluxe added the Enhanced ruleset, which mainly consisted of terrain modifiers, a few additional units, while keeping everything that made the original Empire a hit. I've always had this game on practically every computer I've owned since. It's like solitaire - you can even pick up from games abandoned years back.
What keeps me coming back to Empire? The elegant simplicity, and the excellent random map generator. Most war games degenerate into a unit buildup and rush; in Empire, building up means you're just wasting turns sitting there while the enemy seizes more cities - also, there's a rudimentary efficiency limit which depends on how many cities you have and whether they are busy producing or allowed to "rest". If you build too many units and go beyond this limit, your production time for ALL units will increase.
The ability to play against up to 5 individually-tailored AI players also helps replayability - although the game is sadly lacking in the stats department (it only keeps tracks of your wins and losses, nothing else).
Apparently there's a successor, in the form of Empire: Internet Edition, which is produced by Killer Bee Software, which bought the rights to the Empire name. Last I heard of them was in 2005 although they don't seem to be fully dependant on Empire to keep going, so you'll have to fork out to enjoy the next installment in the series.
Frankly, I would, but right now I have so many other games to play that even Empire sadly gets neglected.
(posted 17 July 2006, edited 10 December 2006)