EDIT: November 2020 wow this really blew up over the years. I have made a direct download available here https://freesound.org/people/wtermini/sounds/546450/ enjoy

Also back in 2012 a wonderful poster was made by Oona Räisänen http://www.windytan.com/2012/11/the-sound-of-dialup-pictured.html
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I was bored so I wanted to see if I could get free dial-up internet so I found that NetZero still has free service so I put in the number and heard the glorious sound of the Dial-up. Remind me of years gone. Unfortunately, I was not able to make a connection.