Bits n' Bytes has whipped up a fairly extensive retrospective for Ion Storm's Deus Ex and Deus Ex: Invisible War, which eventually goes into further detail on Eidos Montreal's Deus Ex: Human Revolution, as well. I gotta go with a quote about the original:
The multi-solution structure was one of the definitive features of the game: if there was a swarm of armed bots at the front of a building, you could hack your way in at the back or, if you had them, throw a volley of EMP grenades to disable them; or, if it turned out, yes, it was a GEP launcher in your pocket and, no, you weren't pleased to see them, you could take the aggressive route. It was all about character choice and that was its beauty: you could play the game the way you wanted to play it. Throw in the fact that your choice of nanotech mod upgrades and skill specialities actually affected your play style in the game, the incredible futuristic Gothic/dismal cyberpunk architecture, and you had boxed magic.
Deus Ex gave you a situation, a variety of items, information, secrets and the certain knowledge that your odds in a straight out fire-fight weren't good. It combined political intrigue and the philosophical demands of the plot, while the choice of ending given to you at the very end was a nice surprise, completely unexpected, unsolicited and enjoyed for what it was, a sly twist in a hugely entertaining game. It was, however, without doubt the plot that carried the game and the unravelling of answers piece by piece as to why the events were occurring.
The graphics were not its strong suit even by the standards of the day (e.g. Quake 3, Soldier of Fortune). They were stiff and blocky, but having said this, that never detracted from the atmosphere. The game also only took place at night and this gave it a genuinely eerie air of mystery. Add to this a strong resemblance to the politics of the day, the incredible secrecy (my god, everyone had something to hide) and the solid comprehensive nature of characters as you compiled information about each one from data-pads and each other, you remember why you loved this game.