Pet Shop Boys cover of Always on My Mind - they take that song and absolutely and emphatically make it their own. It's a masterpiece of uptempo pop with achingly sad lyrics. It was at number one for four weeks in Christmas 1987/New Year 1988 in the UK, keeping off The Pogues Fairytale of New York from the top spot (which enraged some, but which I personally found deeply satisfying, as a Pet Shop Boys fan).
Speaking of Pet Shop Boys, I also rather like this cover version of their classic hit Domino Dancing, by Swedish tribute band West End Girls.