Firstoff... Breakfast here is usually wayyyy richer than in Spain, France or Germany, for example... Although it surely compares with a full oirish breakfast, hahaha...
There are big regional differences, and also depends of course on your wallet. In the street you get something for a cheap as 50 cents. While even in the cheapest restaurant (a Fonda) you will pay at least 3 USD.
You can east pretty any of these during any hour of the day. Tamal or Tlacoyo at 5 PM? No problem. But I would still call them breakfast food, hehe...
So, to the list (I am not going by order, I love them all pretty equally).
Tamales. from 75 cents to 2 USD. My favourites are from Emy, a bit posh, yeah. But the ones with Rajas and the ones with Mole... get a black coffee, and instant heaven. Well, until the GF tells you to clean the house (on weekend), or you have the first meeting (weekdays...) :P
Gorditas de chicharron, preferably made of the blue sweetcorn (mais azul). I prefer Comal to fried, big time. Between 50 Cents and a Dollar and a half. I usually have them with Nopales (the cactus) or quelites. Plus a bit cheese, and red (spicy) sauce. Again, have them with black coffee, and instant heaven (all other comments from above apply, too :P )
Tlacoyos. preferably made of the blue sweetcorn (mais azul). They usually come with Frijoles (beans), requeson (curd) or haba (green beans). The stand just outside of the Mercado Medellin (with Monterrey) is great! Costs? Between 50 Cents to 1 USD. Similar to the Gorditas, you have them with Nopal, cheese and sauce (red or green, hehe...). What to drink? well, black coffee, what else... (insert sign here for instant heaven).
Caldo de res - just a simple stew, made with beef. Gosh... Here, if you want, you can substitute the coffee for a coke.
Huarache, with e.g. cecina. Cost between 3 and 5 USD. My favourites in the Mercado de Jamaica. Where? Close where the flowers are, hehe... Best with a black coffee (imho). Instant...
What many Mexicans love, would be Pozole. I myself eat it, when hungry, but am not crazy for it. sorry :P
And, while you eat these usually in the street... bring some Kleenex. You never know, what sideeffects coffee and spicy sauce have. and paper is sometimes scarce in these simple toilets :D
Typical song for a typical Mexican breakfast? De Itztapalapa para el Mundoooo