"I forgot the password."
Why is a measure word not required in this sentence?
Chinese grammar lesson (of my own): How to deal with a language without articles
In a language with articles, like English, the definitive article "the" means that the modified noun is "the one in the current context". For example, in "I forgot the password", "The password" actually means password of my PC, bank account, or something else. But whatever, it is something both the speaker and the listener know. That is the "context". In some cases, the context is the universe we live in. For example, "the sun". There is only one sun in our universe, so nobody will get confused. In other cases, it is used to emphasize that the modified noun is the ONLY ONE that exists in our world. See the difference of "The god" and "a god".
The indefinitive article "a" means that the modified noun is "an arbitary one in the context". For example, When I say "give me a ball", I mean any ball that is in the listener's hands. Sometimes, The context is a category, and "a" indicates a general reference of the category. The sentence "A panda is an animal" means that every being in the category "panda" belongs to the category "animal" too.
There aren't any articles in Chinese. So all the related expressions must change. Here are the rules:
Definitive article "the"
just remove them.
I forgot the password. 我忘记了密码。
The earth orbits around the sun. 地球围着太阳转。(It's continuous tense, so technically it means "The earth is orbiting around the sun.")
Indefinitive article "a"
if what you mean is "an arbitary one". Then replace "a" with "one". And since you have a number now, don't forget the measure word!
Give me a ball. 给我一个球。
(The) panda is a kind of animal. 熊猫是一种动物。
If what you mean is a general reference of the category, remove "a" directly.
A panda is an animal. 熊猫是动物。
So how can we tell whether "a" implies a general reference or not? Easy. Try to change the modified noun to its plural form. "Pandas are animals" means the same, right? So you see that the number of pandas is unrelated to what you are trying to say.
Your question is like asking why we can just say “the password” instead of “the line/string/etc. of password”. ;-)
But in short: Just take 密码 as a topic, and the determiner “the/my/your/…” (excluding the indefinite article “a”) is implied here. The 密码 can be singular or plural.