Next-Gen.biz has an article from Edge magazine on precisely why the original NiGHTS into Dreams was so fabulous. If you're a Saturn fanboy/girl, you should definitely check it out-- hell, check it out even if you're not.
"Beginning and end become one and the same, an elegant enforcement of the thrill of flying forever forwards. The smooth controls and seamlessly responsive animation was a big part of producing this sensation; indeed, the game came packaged with an analogue controller, a forerunner of the Dreamcast pad. The removal of sterile digital precision is indispensable to the experience, allowing you to achieve the simple thrill of pulling off a fancy move without conscious thought, as if writing your name in the air with a sparkler on Bonfire Night."
Since we've got a new NiGHTS game to look forward to, it's definitely a good time to look back on what made the original so great. It's inimitable and stands out in memory as a solidly-defined unique experience-- in plain English, there's never been anything else quite like it. This piece is exactly what I would say if I had written it first, so go check it out for a warm-fuzzy dreamy feeling.

One element not mentioned in the article was how well the game's music meshed with its surreal, fresh and colorful look. Levels in NiGHTS were more concept than concrete geography; you'd get the vague idea of an outdoor garden, or a seashore or forest, but few specifics. Fabulously, the feel of each level theme would help fill in the spaces; a fresh, splashy sound for a palace of fountains, an earthy, wood-percussive tone for a pavilion of trees. Listening to the music now, I've gotta marvel at how well each track invokes the color and feel of the level in which it was played. Boss fights, too-- these were even weirder than the level proper; again, usually just a configuration of color and shape, so that the idea of what you were doing was clear, while the specifics weren't. You had an idea, for example, that you were fighting a mangy cat with fireworks-- even though the scene was not drawn quite so literally, you could identify its elements through key sensory cues, like the static-fuzzed, hallmark feline arch of the animal's back, or the music, whose guitar wails quite deliberately recalled an alley cat yowl.
Don't take my word for it. Site-I-love, Galbadia Hotel, has the full soundtrack ripped directly from the game-- leech it here.
I've extolled the virtues of NiGHTS previously at SVGL, and posted a few screenshots from the upcoming NiGHTS game for Wii here. I also expressed a hope that, if the NiGHTS franchise is repopularized, it fares with much more dignity than the other raped-to-a-husk-of-his-former-self Sonic Team hero, the titular blue hedgehog. See Sonic's first hostage diary here, and in the second installment, he receives a phone call from NiGHTS here.