UB40 - "Red, Red Wine"
Initially made #34 on the U.S. Billboard Hot 100 in 1984 (it did make #1 on the UK charts the first time), but in October 1988, the re-released version (with an extra verse by Astro) made #1 on the same chart.
Aerosmith - "Dream On" (1973), "Walk This Way" (1975)
Aerosmith's debut single off their self-titled debut LP, "Dream On", only made #59 on the U.S. Billboard Hot 100 when originally released in 1973. It recharted in 1976, this time making #6, when Aerosmith's fan base grew. A similar case occurred with "Walk This Way" (originally released 1975), which made #10 in 1977.