Why?
So will everything else, including the URI being requested, and thus the query string in it. Which is why it makes no difference using GET or POST.
And again, if they are compromised, then they are compromised. It doesn't matter if they have logging disabled, someone who would have access to the logs also has access to either the httpd account or the root account. Either way, they can already read your plaintext usernames and passwords directly when they are being submitted. Of course, they don't need your username and password anyways, as they already have full access to the system.
At least one person appreciates someone taking the time to correct this rather serious misunderstanding.
I disagree from the data I'm seeing in the access logs from my SSL-hosted site running nginx. In the logs I can see lines such as:
GET /path/script?variable=blahblah&another_variable=123
EDIT since I appear to have lost the ability to reply to comments: I disagree with SomeOtherGuy2 that The fact that it may get logged is a red-herring.
Ignoring how secure a server with a rogue user accessing it is, it's possible that there will be more than one server involved in this scenario, and central logging servers are common. Will the traffic sent to the logging server be encrypted? And what if the logging server is compromised? You're essentially storing passwords in plain text.