About these machines:

AnsaFone
Year: 1963
Tech: 2 1/4" tapes (Outgoing Message, Incoming message loop.) Inductive coupling to Bell 500 set. 
Greeting: "You have called an AnsaFone from 1963. Please leave your message after the tone. You'll have about 10 seconds in which to record."

AutoMatic Telephone:
Year: 1980
Tech: 2 1/8" Tapes (Outgoing Message, Incoming Message.) 
Greeting: (The message the machine came with) "Please leave a message after the tone. We will get back to you as soon as possible. Thanks again, for calling." 

PhoneMate
Year: 1983
Tech: 2 Compact Cassettes. Endless loop for OGM.
Greeting: (From the Rockford Files) "This is Jim Rockford. At the tone leave your name and message, I'll get back to you."
https://www.youtube.com/watch?v=SijxE8S6wYQ

AT&T 5500
Year: 1985
Tech: 2 Compact Cassettes. Endless loop for OGM.
Greeting: (From Evan Doorbell's 1980s tapes) "This is Jin White from State Farm insurance. I'm sorry I'm unable to answer your call right now it is VERY important to me. If you'll leave your name and number after the little beep I'll get back to you as soon as I can. Here comes the little beep!"
http://www.evan-doorbell.com/production/Early80s01.mp3

Panasonic EasaPhone
Year: 1987
Tech: 2 Compact Cassettes. Endless loop for OGM.
Greeting: (From Evan Doorbell's "Les' Answering Machine" tape") "Well, it look's like I've missed your call again..."
http://www.evan-doorbell.com/production/Hello.mp3

AT&T 1314
Year: 1993
Tech: Single MicroCasette 
Greeting: (From Sinefield, George's answering machine) "Believe it or not, George isn't at home, so leave a message at the beep! If I was home I would pick up the phone... where could I be? Believe it or not, I'm not home!"
https://www.youtube.com/watch?v=yg-TqEFYcfM

AT&T Digital
Year: 2010
Tech: Solid State
Greeting: (Impersonating Lenny) "Hello! This is Lenny. I can't answer your call right now, leave a message!"