How safe is traveling to Mexico city these days for American tourists?

So many ignorant answers! The problems with the drug cartels are along the border- because the US is the biggest market for them. There are problems in Mexico City, but most don't concern tourists. It's an amazing city. Follow some simple precautions- take taxis from the official taxi stands for example- and you'll be safer than you are in most US cities. I've been in both Mexico City and Moscow, and I was given many more warnings and precautions to take in Moscow. Central Mexico is really lovely- it's a shame more people from the US don't visit because they can't tell the difference between Tijuana and the rest of the country. 

Just BTW, Saudi Arabia is one of the safest places on the planet. I know three Americans living there now who are treated very well, and there is almost no theft or violent crime there. I wish people wouldn't answer questions on here when they don't know what they are talking about!

You already gave a best answer but I wanted to give you my experience, which dates back to January 2020, thus not so long ago (by the time I write this on March 23, 2020). So, Mexico City, well, first of all, I am not American, but Dutch. Physically Dutch and American are hardly any different. Only that Dutch on average are the tallest people in the world, but this will not be noticed. To be honest, I have been in all kinds of buses, taxi's, the metro, just walking at the side road, even alone in the evening, and you know what? I did not felt any more unsafe than I would be if I would walk around here in Amsterdam, The Netherlands. I think the bad pavement is more hazardous than the people. In buses and the metro, where you sit shoulder to shoulder, nobody watched at me with an attitude like, "Yet another stupid gringo", and acted weird toward me. I have stayed 2 weeks in Mexico City and totally 0.0 negative experience. At least not with the people. Be aware this city is 2.2km above sea level and has 20% less oxygen than cities at the coast (Acapulco, Cancun). Also the city lies in a valley, it's surrounded by mountains which means there is a lot of air pollution. The 20% less oxygen I really was not so bothered with, but the pollution affected my eyes. So use eye drops to moisturize your eyes from time to time. All the nonsense you hear in the media about "The drugs in Mexico bla bla", is typical media behavior. Always blowing things out of proportion. Most drugs related issues are in the northwest part of the country, while Mexico City is more than 2,000km away to the South-East. Mexico City is a modern city, people are friendly and like I said, I did not notice any troubles and saw many nice things. Slight minus is the fact most people there don't know the English language, and I was even surprised that at the airport staff over there didn't speak English, which got me into a little misunderstanding with security, because I didn't knew what he was asking me. It turned out my bad was a little to big for the plastic basket :P - So, prepare a little Spanish knowledge.

Not all that safe. Not like it used to be.

When traveling to Mexico, Dominican, Cuba etc I always stay inside the resort as much as possible. Its wayyyy safer inside the resort but you should be fine as long as you stay away from any sketchy parts of the city, touristy areas are safer too

Safer then going to Saudi Arabia, but not as safe as going to Canada

"Yes, Americans can travel safely in most of Mexico, although tourists should be cautious, as in some parts of the United States." ... Acapulco was once a "world-famous" tourist hotspot, but now it is "one of the most dangerous cities in the world that has arisen due to violent crimes."