If it actually had 16382 items on it, broadcast might (or might not - I'm not sure without trying it) be a bit of an issue - actual number of hosts on it now would fit in a /22, but it was enough of a pain re-addressing everything that I thought long and hard about how far it might grow, and then added a couple of bits to be safe. That net has a larger number of users, and more "personal devices" on it - when it was a /24, I ran out of DHCP addresses for 85 users when users started to have a computer, and a phone, and an iPod (or equivalent), and an iPad or other tablet, and an e-book-reader, and who knows what else all looking for an address. Not every user, but enough.
My crystal ball said go absurdly big, but still didn't think I needed to go all the way to a /16. If that one was a /22, I'd be getting close already. The one that's a /22 is an inherently smaller number of users, but I quadrupled it anyway when I had to re-address it for other reasons, as the other one showed me the writing on the wall. I'm pulling for IPv6 to finally deliver the promised land one of these days…
<edit>Similar to Stan, I use the increased address space to apply some logic to my addresses. I used to have that on a /24, but as things grew over 15 years it became harder to manage as the reserved addresses for this had to be used so that would fit. I have both "types of service" and physical location prefixes.</edit>