The first I found in Subzin is from WarGames (1983). Here's the first mention:
00:19:52 - You're really into computers, huh? - Yeah.
00:19:59 - What are you doing? - I'm dialing into the school's computer.
00:20:14 They change the password every couple of weeks, but I know where they write it.
00:20:32 - Are those your grades?! - Yeah.
00:20:35 I don't think that I deserved an F, do you?
Here's a screenshot:
Others:
00:25:35 They might have changed the password.
00:32:15 I put in a password that only I know about.
00:35:32 so I could get his secret password.
00:36:18 If I could just get that damn password, I could play the computer.
00:52:28 The kid broke into the war game using a password left by the original programmer.
00:52:33 - A password? - Yes, sir.
00:52:43 We can find the password and take it out, but it might help to beef up security.
01:36:08 It's like the entire password file has been wiped out.
01:38:15 They've taken out my password.