Accidental Innuendo: Here's the first thing Reala says to a lost and confused little boy at an abandoned theme park in Journey Into Dreams:
Reala: Oh how I've waited for this moment! The opportunity to get you all alone, dear visitor! Now, how exactly should I go about getting what I want? Hmm?
Heck, it starts from the beginning of the game!
Owl: Go over and touch NiGHTS. You'll see what I mean. That is, of course if you're into that sort of thing.
Angst? What Angst?: NiGHTS certainly takes his/her entire species basically being out to get him/her in stride, although s/he does display signs of being bothered by Helen's reaction to learning that NiGHTS is a Nightmaren.
Contested Sequel: Though many people were more or less expecting this thanks to the original game becoming something of a Sacred Cow, Journey of Dreams was a lot less accepted than the original game, with the prime reasons being the Unexpected Gameplay Change of certain levels and the forced, unskippable story. Many agree that this game shows that NiGHTS is best as an Arcade style throwback series that fits better with an Excuse Plot than trying to make an actual "modern" game with it.
Creepy Cute: NiGHTS is a slightly odd example, staying mostly on the "cute" side with big starry eyes and sweet smile. NiGHTS is thinner then any human should be, but very strong-looking, and those eyes could most definitely be uncomfortable; they're a step 'above' cat-like. Combined with the way it moves, it also veers into disconcertingly beautiful and graceful territory.
Crowning Music of Awesome: Pretty much the entire soundtrack, for both games, but especially the songs Dreams Dreams, NiGHTS and Reala, and The Mantle.
Don't forget about Wandering Wildness (the theme for Lost Park) and D'Force Master (the final boss theme) in Journey of Dreams.
Mondegreen: Famously, Reala's line of "Bedishino Naitsu" ("Let's go, NiGHTS") has become "There is no NiGHTS". This one's notable in that many fans used it as a defining element of NiGHTS's and Reala's relationship (and NiGHTS's relationship with Wizeman's forces/all of Nightopia in general) for years.
Nightmare Fuel: Ignoring the fact that you play as a living nightmare (however friendly) and fight other nightmares, the opening cutscenes in Journey of Dreams are pretty creepy.
The scene where Wizeman states his intention to erase NiGHTS' personality, thus turning him/her into an obedient servant. It's also possibly an example of And I Must Scream; at the least, it's a Fate Worse Than Death.
Tear Jerker: In the "Yellow Ideya" ending when NiGHTS reveals that s/he knows that s/he'll die if Wizeman is destroyed, saying that s/he's "known it all along", and then fights him anyway. After Wizeman is defeated, s/he takes one final bow and dissolves into light. Also counts as the character's Crowning Moment of Awesome.
Helen and Will's reactions don't really help.
True. The shots of them waking up and crying, with their tears falling onto whatever they're holding, only adds to the sorrow of the moment.
That One Boss: Bomamba, a witch whom you have to beat by tilting malevolent cat heads into holes. Odd physics mean it's mostly luck if any fall through. It's timed, too, just to add insult to injury. Jackle may also qualify.
And if Jackle doesn't qualify, Wizeman's battle in the first game definitely does. The fireballs and giant snowballs are easy enough to dodge, but the rows of stones will trap and kill you if you misjudge their movement. The worst is the tornado formed like a time glass — there's a small hole right in the middle of it, but you can only fit if you Drilldash, and it's very easy to miss.
Chamelan is a Guide Dang It sort of boss. Once you know what to do, executing it isn't too hard... so long as you don't dawdle at all and have reasonable luck.