This remains one of the few games I've come across where you can "do anything" and not have it feel like a sandbox. It's completely different from the GTA III model or even the Elder Scrolls model, where the quests are optional. The stuff you do in Deus Ex is not optional; how you choose to go about it is.
The whole "Killing Anna" event is a perfect example of just how far the designers were willing to take this concept.
Anna Navarre is a major character in the game. She's your superior in the police force, and is supposed to be able to curbstomp you at will, so when she orders you to kill a prisoner at one point, your character makes an objection on legal (and maybe moral) grounds but it's not like the obvious option is to kill her instead. The game never indicates this outright, but builds a scenario where you might try it.
After a heated battle to capture the leader of a terrorist cell, Anna orders you now shoot the unarmed prisoner, and furthermore demands you stop talking to him right as he's telling you all kinds of interesting stuff. You can keep talking to him, and she gets more and more pissed off as you do, eventually claiming she's going to report you to the Chief (which she does indeed do if you let her live, and you catch holy hell for it). The prisoner is saying things like "If you leave me here, she'll kill me. This'll be the last time you see me alive."
At no point does he even suggest you kill your superior officer to save him, but the thought has probably already been planted. It's left entirely up to you to just try it and see if it works.
It sounds completely ludicrous, though. By all laws of game design, you shouldn't be allowed to kill off a major character so early in the story, especially when she's still got a ton of scripted stuff she's supposed to do. But sure enough, should you unload on her sufficiently, she dies! (And, amusingly, explodes! -- Try not to kill her too close to the captive or you're going to be bringing him back to HQ in a bucket.)
It really seems like it shouldn't work, even with all the hints dropped in the writing. This is one of those "only in videogames" things you do to putz around and see what happens, like shooting your friendly characters in World War II sims or making time paradoxes by killing Ocelot in Metal Gear. Best you're hoping for is an amusing game over screen. To be honest, that's the only reason I thought to do it my first time through. I was never expecting it to actually work. Amazingly, it did.
Blow up Anna and Deus Ex won't even skip a beat. The game simply keeps going and dramatically re-shifts the plot to compensate for what should've been a game-breaking action. That was the moment when I became permanently hooked all those years back. I'd never seen anything like that in a game before, and nothing has had quite that level of holy shit-ness since as far as plot goes. Some games have come close, but never since have I felt like I was able to get away with something that wasn't supposed to be allowed, and have the game not only allow it, but incorporate it flawlessly into the plot.
While the canon plot of the game doesn't have this happen, the incident is certainly not brushed off. It becomes a major plot point as your first big betrayal to UNATCO, and Anna's ex-partner will never let you live for it. He eventually discovers what happened and hunts you down for the rest of the game. Oftentimes in cutscenes you'll take off via helicopter only to see Gunter run in at the bottom of the screen and take a few potshots at the departing chopper. He rants and raves about your terrible betrayal and laments the loss of his parter.
The Anna-killing thing isn't the only one either, just the first that players are likely to stumble into. If you fully explore the game, it's loaded with this kind of stuff. You can completely gunk up the default plot by being a total tin-foil-hat-wearing bastard. Explore everything and trust no one, because there really are conspiracies around every single corner. Paranoia is not only justified, it's encouraged and rewarded with some frequency. Stuff that you're not supposed to know right until the endgame can not only be discovered, but completely diverted mere hours into the beginning of the game.