As I used to work for ups in Sweden (employed by a company that ups have hired due to lack of personnel, but still in their main terminal) I do know how things work. The packages are definitely put under a lot more strain if shipped by ground than by air, so chosing the express saver option if shipping international (or I between states if you live in the US) is something I would recommend if the package is fragile.
What most damaged packages have in common is that they are poorly packaged, so you need to make sure that the packaging is appropriate for the size and weight of whatever item you're shipping. There shouldn't be any "air" inside the package so that the item doesn't move around, destroying the actual packaging and perhaps the item itself. With proper packaging, which definitely isn't hard to achieve, the only threat towards whatever you're shipping should be random accidents, which almost never occur in my experience.
It's important to keep in mind that packages are never treated as if there was a pair of $1k headphones no matter how many stickers of FRAGILE you put on the box or no matter which parcel service you choose to use.
