I remember listening to WCBS-FM in New York, but by that time the station was just like any other mediocre Oldies station, and no one ever really stood out to me on air.
WFMU's "Music to Spazz By" and "Teenage Wasteland" are both great shows, "Three Chord Monty" is good too. I didn't really hear about that station till I was packing shit up and moving to Colorado 5 years ago, but it's the oldest freeform station in the country and 100% listener supported.
There's a show out here that broadcasts on the University of Colorado station (1190 AM Boulder) "The Lunch Hour With Jonny Trash". The show features mainly classic punk rock stuff, and most of it people are very familiar with, but it's still really cool to turn the radio on and hear the Buzzcocks or Television...
"Route 78 West" is a great show that specializes in rare country/honky tonk. One of the hosts has a large collection of rare 78s and records alot of good shows that come through town. "Honky Tonk Heroes" on KGNU (88.5 FM & 1390 AM Boulder/Denver) is another good show that plays alot of obscure and popular country/honky tonk/hillbilly music.
I think it's gotta be an independent station nowadays.
Growing up in Miami Florida in the '60s we had two great AM stations: WQAM / Tiger Radio and WFUN. They had a bunch of jocks like Rick Shaw and a slew of others I can't recall at the moment.