Seinfeld- Jerry and Elaine are exes and breify get back together at the end of season one
Friends- lots of romantic entaglements but mainly Chandler/Monica, Ross/Rachel, and Joey/Rachel
How I Met Your Mother - two of the main characters are a steady couple, the other three are a love triangle
Big Bang Theory- by the end, it’s three couples and one single guy
Any shows like these where the main characters never date each other or hook up with each other?
Mac is gay for Dennis, and Charlie and Dee had a fling in The Gang Misses the Boat
Addressed the Charlie and Dee thing below; I just don’t consider a one-off, single-episode B-plot like that 10 seasons into the show (with a later throwaway joke in one episode three seasons later) a “romantic entanglement” for what’s an ongoing 17-season comedy show.
Mac’s crush on Dennis is the closest we come, but that’s still very distant from “romantic entanglement” to me; that implies an entanglement, where in reality Mac’s one-sided crush is infrequently referenced and pretty much always for laughs, and Dennis clearly demonstrates at every turn that literally nothing will ever come of it. The audience is always deliberately shown that this will never turn into anything; there’s no “will they, won’t they” going on because the answer is always and in perpetuity “won’t they”.
TL;DR: There’s no actual arc or plotline.