Adobera- Jalisco-style queso fresco that's sold in blocks (hence the name- adobe bricks). It's good for melting and is mild. It's perfect for queso fundido. I suppose you could try substituting Monterey Jack and I use it whenever I need some sort of mild cheese, or in a pinch, mild cheddar, although it's nothing like cheddar. Some say a mild feta is a good substitute, but it would have to be a very mild feta.
Oaxaca (or quesillo in Mexico City)- String cheese that's coiled into a ball. It melts nicely too and is stringy, so it's a good idea to pull it apart with your fingers before you melt it. You could use Mozzarella instead, and I use it in place of Mozzarella here. But Oaxaca cheese is more fun.
Cotija- This either comes as a fresh, salty white cheese; or it's aged with a creamy color and a yellow rind. It's much easier to find fresh Cotija (the name comes from the town in Michoacan where it apparently originated) than aged. Feta can be a good substitute for fresh Cotija (and I use Cotija in place of feta here) and Parmesan is similarish to aged Cotija. I love aged Cotija on pasta.
Chihuahua- I don't use this one much since adobera is more popular here and I can't tell enough of a difference to make it worth tracking down Chihuahua cheese. You can use a very mild cheddar or Monterey Jack instead.
Panela- I don't get this one very often either. It's very slightly similar to paneer (sort of between chana and paneer), although it doesn't hold its shape as well when you fry it (you can barely fry it, although it is possible).
Requeson- This is similar to ricotta and I use it in place of ricotta or cottage cheese. It's not salty and it goes well with lots of things.
Manchego- This is not what you'd buy in Spain, or at Trader Joe's. I like it, but we generally buy something else. It's white and mild and melty and mostly like Monterey Jack.
These last two aren't cheeses:
Crema- Sometimes this is called Mexican sour cream, but it's more like creme fraiche. I think it's similar to smetana. I do use it in recipes calling for sour cream, but I wouldn't substitute the other way around. You could try cream with a little sour cream stirred in. Or make your own. I love this stuff. I've also used it in ice cream. Or just mix it with strawberries and a little sugar.
Jocoque- This one can be a little confusing. Here in Jalisco it's a fermented sour milk product that's drained and very creamy. It's not impossible to substitute plain yogurt for it, but it's really not the same (I've tried it). It is not like tvorog, although it's more like quark. They also sell Jocoque Arabe here which is pretty much plain yogurt. I'm guessing since the two are fairly similar that the name (it's a Nahuatl word and refers to an indigenous dairy product, according to someone on Wikipedia) was transferred to yogurt after many Lebanese moved to Mexico. If you know more about jocoque, I'd love to hear it. Here's what I love to do with it.