first-come, first-served
Served. The people are being served, not serving.
-
Wrong: First come, first serve.
Right: First come, first served.
The whole phrase is passive: the first to arrive is the first served.
The logic
Both halves describe what happens to the person: they come first, they get served first. Dropping the -d turns the second half active, which now says the first to arrive has to do the serving.
Nobody thinks that’s what it means, which is precisely why the missing D survives—the phrase still communicates perfectly. It just isn’t the phrase.
Now go put the D back.