I can think of a few:
The classic Sonic Trilogy
(Requires no explanation).
The Classic Streets of Rage Trilogy
(SoR3 JP please, don't sully my games with artificial difficulty to try to curb rental clears).
ESWAT
(Cooler and grittier than the arcade counterpart).
The Super Shinobi Duology
(Revenge of Shinobi and Shinobi 3,
but allow me to be pedantic and use the Japanese names to keep things tidy).
Gunstar Heroes
(Legendary, needed to be longer, or a sequel on the same system).
The Road Rash Trilogy
(2 and 3 are more fun than the first)
The Strike Trilogy
(Desert, Urban and Jungle Strike)
Ranger X
(Beautiful visual tricks here)
Phantasy Star 2, 3, 4
(That one is rocky, only 4 is truly polished enough to be a classic IMO)
Strider
(Strider 2 for the Mega Drive doesn't exist, it's just a bad dream)
Rocket Knight/Sparkster
(Super confusing franchise split between the MD and SNES with very
different games, but all excellent).
Contra Hard Corps
(SNES lovers will hate me, but this is the finest Contra by my reckoning
JP version is kinder, so I prefer it because I'm not so hard core(ps).
Pulseman
(Creative platformer from Gamefreak before they were stuck churning Pokésludge for the N overlords.
Can't beat the greats, but worth a play).