If we're excluding motorsports, where the sky's the limit, then probably any equestrian sports. Even if you're renting someone else's horse (which I don't even know if this is possible, but I'd bet it is) it's going to be expensive, and certainly if you own your own horse, pay for boarding & training/conditioning, pickup truck & horse trailer, plus whatever the event fees are.
My parents used to live next to an equestrian center and every other weekend when the weather's nice you'd see a bazillion dollars of trucks & horse hauling stuff along with plenty of RV's, since it's almost inevitible that some percentage of people who do out of town events will want to buy an RV so they can sleep on-site instead of searching for a hotel in each town.
Granted, it's still a pretty cool way to spend money if you've got the free cash but the costs have to be way up there. I'm not sure if sailing is considered a non-motorsport either, but I had a boss that was into competitive sailing and I know that can easily get quite expensive as well for similar reasons to anything with horses.