Believe me, you have better odds of being safe in the Metro than taking a taxi/metrobus and it will be faster & cheaper than any of the other options.
You can get around by taking one of the regulated taxis as @hippietrail suggests, however in Mexico City you HAVE to take the metro at some point, so there's pretty much two options: take it now or take it later, but whether you think it's insecure that's another matter.
Report of theft in the metro is actually the same as any big city and pickpocketing is actually lower than in some parts of Europe such as in Paris, the Wikipedia article for Mexico city even lists a non-referenced paragraph that states that Mexico City is actually safer that Washington DC & Moscow.
To add some stats to the above comments, here is a chart (in spanish) from 2010-2011 about the number of thefts per transportation system:
Chart per transportation system in Mexico City
As you can see, the metro is actually the lowest and even when the theft to vehicles (asalto a vehiculos) is pretty high, the article states 1 every 300,000 vehicles gets mugged. As for the metro, the same article states that "Matemáticamente, la probabilidad de ser asaltado en el metro cada día es 1 en 15 millones.", meaning, the odds of getting mugged in the metro is 1 every 15 million. It would seriously be a lot of bad luck if something happens to you in the metro.
Being the above being said and comparing to the warning issued by the US Travel Gov site to say, similar large metro networks such as France's: France crime; you can guess that Mexico City is like any other major city in the world where you have some odds of getting mugged or pickpocketed specially if you do not look from around and you find yourself stopping & staring at a map on every corner.
I am not exactly sure where you are heading to, since the Metro in downtown Mexico City involves quite a lot of metro stations, but here is a map of the most recurrent thefts in Mexico City by location, issued by one of the largest newspapers in the country (keep in mind that although the map looks kinda crowded, you are looking at a 21.2 million people city according to Wikipedia):
El Universal / Google Maps - Mapa delictivo del DF
My last advice is that Mexico City is quite a wonderful city to visit too, and although I won't lie - there are some chances of you getting mugged or pickpocketed, the odds for you having a very pleasant trip are a lot higher, specially if you speak spanish.
Take precautions as in any other big city you would be travelling into: beware of really crowded metro stations (if you are not in a hurry just wait for the next wagon), keep ipods/cameras/cellphones hidden, have copy of your passport / most important documents attached to your body and you should have an awesome time in Mexico.
Hope the above helps.