Due to popular demand the below text has been made into it's own thread and stickied for easy reference.The series started as the "Wonderboy" series, as developed by Westone for SEGA. Due to licensing issues what with SEGA retaining the rights to the "Wonderboy" name and Westone retaining rights to the actual game, the games are named something different on nearly every platform they were ported to. Sometimes they even differ in name on the same platform, between regions.
Without going into things too much, here's a quick legend for you:
Wonderboy (1st game)
Wonderboy (SMS)
Adventure Island (NES)
Wonderboy in Monsterland (2nd game)
Super Wonderboy in Monsterland (SMS)
Bikkuriman World (PCE/TG16 JP)
Wonderboy III: Monster Lair (3rd game)
Wonderboy III: Monster Lair (PCE/TG16 JP, Genesis)
Monster Lair (PCE/TG16 US)
The Dragon's Trap (4th game)
Wonderboy III: The Dragon's Trap (SMS US)
Monster World II (SMS JP)
Adventure Island (PCE/TG16 JP)
Dragon's Curse (PCE/TG16 US)
Wonderboy V: Monster World III (5th game)
Wonderboy V: Monster World III (Genesis JP)
Wonderboy in Monster World (Genesis US)
Dynastic Hero (PCE/TG16 both regions)
There are other platforms these games appeared on, but I listed the main/most common ones here. Only the first game saw a port on the NES. Speaking of the first game, it's also the only game that didn't make it to the PCE/TG16. The Turbo game New Adventure Island is very similar to the first Wonderboy, and it could be viewed as a "remake" of the original with greatly improved graphics (added parallax) and level changes. Some of the level cues are taken directly from the first game but it's not a straight port by any means.
As you can see from the list, "Adventure Island" on the NES and "Adventure Island" on the PCE were actually ports of different games in the series. You might also know that 3 sequels were made on the NES (Adventure Island 2, 3 & 4). These games have nothing to do with the "Wonderboy" series and were spin-offs done by Hudson (not Westone). This spin-off series continued on the SNES and eventually the Wii.
There was a 6th game on the Genesis called "Monster World IV." The "Wonderboy" name was dropped from the title on that final game (probably because the hero is a girl) so it's technically not a part of the series.
Screenshot ComparisonsWonderboyLeft to right, top to bottom: Arcade, SEGA Master System, NES (Adventure Island), TurboGrafx-16 (New Adventure Island)