Sonic 1 has a bunch of these to varying degrees:
The ascending bassline in
Bobby Brown's Every Little Step shows up at the start of
Spring Yard Zone. It's debatable, but there's enough stylistic similarity between the two songs that I'm willing to argue it's the source.
Andy Williams' Music To Watch Girls By has obvious similarities to
Marble Zone.
The first half of the synth line running throughout
Duran Duran's Planet Earth is a close match for the opening bars of
Final Zone.
Blade Runner (End Titles) by Vangelis is so clearly the source for most of
Scrap Brain Zone that it hurts. Same basic chord progression and similar instrumentation all the way down to the occasional timpani fill.
There's also an easy one in 8-bit Sonic 2: Compare the
boss theme with
808 State's Cubik.
Going the other way, most people know that Sonic 2's ending became
Sweet Sweet Sweet, but Nakamura also turned Green Hill Zone into
Marry Me and Starlight Zone into
Kusuriyubi no Kesshin. At least he owns the source material in all three cases.