A motif is a musical idea that occurs multiple times throughout a work or across multiple works. Within the scope of this website, "motif" refers to a melodic motif, as opposed to a rhythmic or harmonic motif. (The motifs in Undertale seem to be mostly melodic in nature, and melodic motifs tend to be more distinctive and easier to recognize in general.)
Note that there is a difference between a motif and a leitmotif, the latter specifically meaning a motif that has a thematic meaning within the work. For instance, the melody John Williams's "The Imperial March" is not only used throughout the Star Wars saga but associated with the character of Darth Vader specifically. Many of Undertale's motifs certainly are leitmotifs, but for some, any thematic connection is tenuous. This website uses the simpler term "motif" so as to classify recurring motifs in the soundtrack without having to speculate as to whether they represent anything in particular. (But of course, I have also provided said speculation to those interested.)
This is a website that provides a list of motifs I've found in the soundtrack to Undertale. I've given each motif a name and description and listed the music tracks it appears in, with timestamps for each. Some motifs have multiple variants; I've provided sheet music and a MIDI file of each. Lastly, some motifs are based on other motifs, and some tracks are simply distorted or altered versions of other tracks; this website lists those.
I've seen videos listing several of them and demonstrating where they appear, but a cursory Google search only revealed one link to a website claiming to have a list of them, and the link was dead. My goal is to have a sort of one-stop shop for Undertale motif info, i.e. to have the most extensive database.
Go ahead and message me on Reddit. I won't guarantee that what you provide will be added. Every track from the Undertale OST is in the database already, but there may be other tracks that are tied to the game somehow that deserve mention (e.g. Noisemaster's Theme from Cucumber Quest is included because it's the origin of one of Mettaton's motifs). For motifs, I want to know that the motif appears in multiple tracks in a nontrivial way before including it (because otherwise it's not a motif, it's just part of a song).
The release of Deltarune ch. 2 is what motivated me to make this website, but the list of Undertale motifs and connections was all there already, in a folder on my computer. Adding Deltarune is going to be a more significant undertaking, because that's another 86 music tracks to analyze (and more in chapters 3-7 once they come out!). I do currently plan on getting to it eventually, but like Deltarune itself, I don't want to specify any particular timeline.
There's an additional complication, too: Deltarune seems to include at least one or two motifs that aren't purely melodic. (In particular, I've noticed that the King's and Queen's themes contain a very similar chord progression.) So expanding this database to include Deltarune also means expanding it to include other types of motif.