Paul:
The reason many courses have a 19th hole is because they couldn't make a longer hole get all the way back to the clubhouse, and because either the architect or the client rejected the idea for a par-3 18th. At Stone Eagle, I suggested our 19th hole for the opening or closing hole, but the client thought that would be too odd. Yet they loved the same hole as a 19th.
Or, occasionally, the client suggests that one put in a 19th hole, and because you're already close to the clubhouse, a short par-3 is all you can fit in.
I actually had a potential 19th hole for the new course at Dismal River that was a short par-4, playing back up to the road. But it was very steeply uphill, and I thought it would take away from our great finishing hole, instead of enhance it. Plus, it would have cost another $100,000 or so to build and irrigate.