This dovetails with my post a few weeks ago looking for non-violent books, since another common fixture in my writing is violence-based conflict. Also, conflict on a huge scale. The fate of the world hangs in the balance! I want to scale down, to write about something important but not earthshaking, interesting but not epic.
So far, I don't have many ideas.
The most obvious one is a literal race: characters competing to reach a physical goal. It doesn't have to be as simple as a horse race or a car race: "Rat Race" showcased one way of injecting variety into the "race" premise.
Other kinds of sporting events have a similar time-limited nature. I don't really like sports, and most don't translate well to written form, but possibly a fictitious (fantasy or futuristic) sport could sustain a story.
Another possibility is a "race for treatment" -- one real-world example of this would be getting a snake-bite victim from the jungle to a hospital. Still, I'm wanting to steer away from life-or-death scenarios. A fantasy example might be "get the faerie back to the portal before it closes at dawn or she'll be stuck here on Earth for ten years" -- where failure is bad, but not fatal.
Then there's "you have to stop X event from happening at Y time". Classic ones are "stop the meteor from hitting the Earth" or "stop the bomb from going off", but less dire possibilities exist. For example: Lily is marrying Damon tomorrow, but Lily's ex-boyfriend suspects Damon's lying to her. Can he get proof that Damon's really a sleazeball before it's too late? In a similar vein would be political scenarios: "this treaty will/won't be signed unless the protagonists are able to provide certain information by X time."
Anyway, not sure I have anything I really like yet. Anyone have ideas they'd like to share?