Hiya, I must be in the totally wrong part of the city, but in the last few days I've not run into anyone at all- I'm even the only person in my hostel 
If anyone is currently in town and would like to meet up for a drink etc, please drop me a line. This is a very cool city so it's a shame to miss the nightlife! 
Most tourists stay in the Pink Zone which is relatively safe. Even then I was in a club there and a big fight broke out when some Mexican couldn't or wouldn't pay their bill.
Mexico has had lots of trouble in the last several years and many now give it a miss till it settles down again.
Do be very careful of pick pockets, especially on the metro.
^ Thanks. Although pretty ironically, just as you wrote that our hostel in the "pink zone" got burglared and some people (including me) lost all their stuff. Though that wasn't the point of my posting- I am very much ok going out on my own, its just that sometimes it's nice to have company to talk to!
Otherwise I have found Mexico pretty safe, I must say, although horror stories of cab drivers seems to prevail. Easily avoided though by not taking any!