Set the WayBack Machine to... Tuesday, 20 February, 1962 - 7AM EST
Listen to the John Glenn Orbital Flight as heard on KCBS Radio
Glenn_KCBS Pt.1 -- pre launch thru most of first orbit *** 
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Glenn_KCBS Pt.2 -- end of final orbit thru splashdown and recovery *** ***
These are fairly large files... broadband access recommended!
Feel free to copy these for your own use... please do not sell or otherwise exploit these historic recordings!
Thanks...
Marshall
NASA, wouldn't you just know it, also has audio from the MA-6 Flight... which you can find on their:
On Board Recording of John Glenn During Friendship 7 Mission page.
This is also long-form audio, in somewhat "bite sized" chunks - Java and RealAudio formats.
Also included on the above NASA linked page are further links to other MA-6 related pages including transcripts of all the in-flight audio.
Back in 1962 the actual mission audio was played back to the radio & tv stations by tape delay... and there was no NASA-TV or an audio equivalent that one could tune into to hear live mission audio.
And yes, people were excited enough in 1962 to get up at 4AM (on the West Coast) to follow the early space flights... on the radio, no less! Today, if you want to have a front row seat to the Human Spaceflight adventure, just get hooked into NASA-TV and enjoy the Final Frontier!
ps: NASA TV is running a lot of Project Mercury archive stuff today (20 Feb 2007)