The Stranglers - Walk On By. Absolutely brilliant. The only version where you really feel the pain of the separation.
If you say so. It's not bad - the Isaac Hayes one is better though, I reckon. However, for me, the Dionne Warwick original is perfect in every way from the vocal performance to the arrangement by Burt Bacharach and the typical understated brass. That's not to say people shouldn't cover it, but I can't see how it can be improved.
Of the same era, undoubtedly one of the best covers is of course 'Respect' by Aretha Franklin. The original by Otis Redding is good enough but it's a bit pathetic - Aretha turns it into an absolutely huge feminist anthem such that you can't even imagine any more that it was intended to be sung by a man.
I also quite like The Who's version of 'Summertime Blues' (one of their signature live tunes of the 60s). The Monterrey version is great. I am not sure that it beats Eddie Cochrane's original though.