The greatest risk you face in DF is the drivers. Be very, very careful crossing the streets - whatever rules of the road nominally exist are usually ignored.

That being said, I don't feel particularly unsafe in Mexico City, but I also speak Spanish and have a lot of experience traveling and living in Latin America.

When I'm in the city I try to steer clear of taxis - particularly ones on the streets - and take public transit everywhere. I feel much more comfortable on the Metro or even a pesero (i.e., minibus-type thing) than in a taxi because there are other people around. Mexico City has a really good transit system, and the subways actually remind me a lot of the ones in NYC. However, I know rather well-off locals who will blithely jump in a Beetle taxi cruising down the street in Polanco, and they haven't been killed yet.

I think if you stay in one of the nicer, central neighborhoods (Zona Rosa, Polanco, Condesa, Colonia Roma, Anzures, etc.) and don't wander aimlessly down side streets by yourself at weird hours of the night you should be fine.

Keep in mind that DF sees absurdly few tourists. When I've been there, the only foreigners I ran into either lived/worked there, or were American high-school kids on some kind of church-run, convert the poor people trip. It's a shame because the city is truly fascinating - but most Americans are either frightened of it, or just visit Mexico to get drunk by a beach.

Another cool thing about DF - it makes NYC look and feel like Indianapolis. Seriously.