Composer Junko Tamiya (credited as: Gonzou) is the mastermind behind these melodies. This game came quite a bit later in Tamiya's career than Bionic Commando, which appears to be the game she's best known for. But there's definitely a reason why Capcom is quoted saying she "was very talented." And even though it's short, sweet, and to the point, I would have to characterize the Title Theme, as part of this talent.
The great thing about game music from this time period was that while the cartridges and such could not handle massive orchestrations for each game, the music was very intricate and special in it's own way. To this day, chip-tune style music is widely sought out because of the distinct sound. And Little Nemo delivers these sounds perfectly. I know that I've said this before, and it still remains true that Title screen and file select screen songs act as portals into the music world the player is about to be swept away in. This is perfectly illustrated by Tamiya's work in Little Nemo. The melody is playful and wonderfully embellished with some cleverly laid out harmonies and chord progressions. Just loop it! Over and Over again! Don't tell me that didn't put a smile on your face and make you want to climb inside a big lizard and crawl up trees!
Now I did find a couple remixes of the title music here on the web but I wasn't particularly impressed with either one myself. I will go ahead and list the one of them that I still thought was cool in a sense that it was pretty well laid out for guitar; just having some minor rhythm issues:
Thank you again Addison for bringing this game and it's amazing soundtrack to my attention. I think it's safe to say that I will probably be doing many more blogs about this game and Tamiya's other works. She did an excellent job capturing a childlike adventure and wonderment in this 8-bit dream.