I cannot speak for Facebook, but I can for Vicigo!
tl;dr: No, we do not know your password.
However, the answer is somehow more complicated than this. We still have to store the passwords, so you will be able to login again. But what we can see is just the encrypted version of your credentials.
When you submit the form on signup you send us password, which is immediately encrypted on the server by a hash function. What it does, it accepts your input which may be something like adrian123 or ilovevicigo and then, the encrypted result $2a$08$O...(and 30 other characters) is stored in our database, which we can view at any time but cannot really say what does the string stand for.
This is one of the highest standards in data protection and even though the facebook password storage technics are probably more sophisticated than Vicigo's, I am sure that they are still based on the concept of hashing algorithms.