Fushigi no Yume no Alice > NEC PC Engine

In the excellent Fushigi no Yume no Alice you take the little girl called Alice through strange and dangerous forests, caves and even castles doing battle against the deadly creatures that try to attack her. Use her powerful scream to wipe out enemies, but be careful not to overuse her voice or she'll be left panting trying to catch her breath. You can also use her agility to jump on enemies to eliminate them and make it to the big end of level bosses.

Adventures don't come any better than Alice in Wonderland, but there are plenty of other titles to test your adventurous streak on, such as Rayman 2 - The Great Escape, Rayman and the collection of classics that is Namco Museum Vol. 1!