I've only just heard this story, in a reference on another thread. I'm very interested, since it happened not far from where I now live. Yes, there is significant variation on the details in the various retellings, including the "Fun to know about Ghosts" account, which - despite the quotation marks - was obviously watered down for kids.
Assuming Savalas, in the television segment, was (a) telling the truth and (b) fairly accurate in the details he seems certain about, I want to clarify some obvious inaccuracies in the version that Diabolik8 related at the beginning of this thread. (It looks like a number of other posters were aware of a more accurate version of the story but didn't directly address these details.
Savalas was not traveling from a friend's house on Long Island to New York City. He was coming home to his home on Long Island after dropping off a woman he had a date with. Presumably she lived somewhere in New York City, which could be in Staten Island, the Bronx, or Manhattan, but might also be in Brooklyn, or in Queens (where he ran out of gas) - both of which are actually on Long Island. If he was still living in his childhood home (he mentioned he spoke to his mother) Telly was living in Garden City, a little farther east in Nassau County.
It wasn't an all-night café, it was a White Castle. As mentioned by genex17, this was a popular early fast-food chain.
Harry Agganis was not the name of the mysterious driver. The driver identified himself as James Cullen, according to Savalas. Although Savalas doesn't specifically say so, many have come to the conclusion that Harry Agganis was the baseball player that Cullen said he knew - and who apparently died that day.
Savalas's wallet wasn't missing, but he was apparently short on cash.
And a few observations:
Although Savalas says he thinks it happened in 1958 or 1959, Agganis's death was in 1955, which I think is more in line with Telly's time working at the State Department.
The White Castle closest to the Grand Central Parkway near where it meets the Cross Island Parkway is at 175-28 Hillside Ave., about a mile and a half from the intersection where the gas station was. I wonder if anyone out there can confirm the surrounding area was more wooded than it is now. It seems strange that he was on a busy local road, rather than on one of these expressways, when he ran out of gas, but the location of his home and the possibility his date lived nearby makes this less questionable. Of course there may have been a closer White Castle back then; the chain has lost some market share. Again, maybe someone can research this.
It would be interesting to see exactly how the Journal-American - the paper Telly mentioned - covered Agganis's death. It's possible he confused it with the Long Island (Daily) Press, another popular broadsheet in the area.
I find it interesting that Savalas's full first name was Aristotelis, and Agganis's was Aristotle. Maybe Cullen was just trying to say he had Greek friends.
I haven't read much on the 1963 addendum to the story, but will soon.