I also coincidentally just rented Midnight Cowboy.
Jon Voight struck the right notes as the naive Joe Buck, but it was Dustin Hoffman's Enrico "Ratzo" Rizzo that really made the film.
There's a reason Hoffman gets top billing. He's in a class by himself.
My grandmother's always compared it to Easy Rider, and I understand why: same year, each starring two up-and-comers who went on to become legends (well, three in the case of Easy Rider, with Jack Nicholson), both stories of the death of the American dream set against the backdrop of traveling across the country and the atmosphere of sex and drugs that characterized the era, filmed sparsely and with a small cast. And of course they're both goddamn masterpieces.
I would add that the two leads had something of an Oliver Twist/Artful Dodger relationship.
I would also add that the only reason I can see why the movie was originally rated X (trivia: the only X-rated film ever to win Best Picture) was the very non-explicit gay sex scene (and almost equally non-explicit homosexual rape scene). This Film is Not Yet Rated had quite a lot to say about the MPAA ratings board's bias toward male, hetero sexuality. (Wikipedia says UA self-applied the rating after the MPAA offered an R, but doesn't cite a source.)
Going to have to let this one sit for awhile and give it some thought. But I'll summarize by saying it's one of those classics that everybody should see.
Speaking of which, next one in the queue is The Godfather, which I have somehow gotten this far without seeing.