QC is not an adventure comic, or a mystery solving comic, etc. And it's not like Jeph doesn't write non-romantic plotlines (mostly anything to do with Hanners, but also like Faye's backstory, Vespa Girl... uh... okay I can't think of anything else...)
Let's see...
- Every comic that existed as of when I found the site (i.e. all of the original 100 or so) and at least the next 100.
- The arcs involving Faye's sister.
- The brief karaoke wars run, which did admittedly lead to a romantic plot.
- The drunken sledding arcs, which admittedly contained minor references to romantic plots as a minor part of them.
- Every single strip involving Hannelore.
- Every strip involving both Hannelore and Marigold, particularly the earlier ones.
- Every strip involving Raven without the hobo boyfriend or makeout hobo.
- Every strip centered around Pintsize.
- The arc with Marten looking for a job in the first place.
- The buying a guitar arc.
- The plot involving the band.
- Jimbo's very existence.
- The arcs involving both Marten's mom and his dad.
- Marten meeting Dora's parents.
- Everything in which Sven discussed his music.
- Sven's intern.
- Everything in which a major character gets injured (remember the punching intern?).
- The rivalries at Coffee of Doom (i.e. Faye vs. Raven; Faye vs. Penelope; Pen's "philosophical" rants; "Two girls enter, one girl leaves," etc.)
- Faye and Penelope exercising.
That's off the top of my head.