Karen, I love to use white pepper in certain dishes, mostly either for appearance - I don't want black flyspecks
in a white sauce - or for flavor, when that distinctly different gentle-but-pungent white pepper flavor is what I'm after.
Oddly, though, I've never thought about getting a dedicated grinder. Instead, I have a small porcelain mortar-and-pestle at my kitchen work station, and when I'm needing white pepper, I grab a few pepper corns and grind to order.
The other one that comes to mind is Sichuan peppercorns, which I think is a different botanical family than the true peppers, but they sure look and act like peppercorns! I always dry-toast them in a small black iron skillet, then grind. It keeps well, so I'll usually grind an ounce or two and keep it in a small airtight vial. Just used some tonight for Ma Po Tofu!