I buy and sell a lot of guitars and have learned how to (and not to) pack a guitar for shipment. These simple steps can go a long way to making sure your beloved instrument gets to its destination safely. The more effort you put into properly packing the guitar, the better off you will be. And yes, while it takes a little more time, care and attention to do it right, you'll be better off than if you have to spend the time explaining to your insurance agent why they should reimburse you for your poorly packed guitar.
Only ship the items needed. If capos, picks, cables, etc. are in your gig bag or guitar case remove them.
Be sure you have the proper packing material. You will need two boxes, lots of bubble wrap, shipping tape and newspaper.
De-tune your guitar to reduce neck strain.
Wrap various parts of the guitar with bubble wrap separately. Start with the head stock, then do the neck, then do the body. You can use large rubber bands to secure the bubble wrap and/or packing tape.
Place folded newspaper between the strings and frets.
Place folded newspaper between strings and pickups.
If you ship the guitar in a case and it doesn't fit snugly, consider using bubble wrap or other packing material to fill the voids.
Wrap the case or gig bag in bubble wrap. Place this in the first box and fill out with packing material. Then shake it gently to listen for movement. If you hear something, stop, start over and add more packing.
Place the first box inside the second box and fill the voids with bubble wrap.
Perform the shake test again and if you hear something, start over and add extra packing material.
Use packing tape (not household or office tape) to secure the box. Use more tape than you think you need. Better to be safe.
BONUS TIP: DO NOT USE PACKING PEANUTS - they don't offer enough protection and are messy as well as bad for the environment.
Lots of this is just common sense. Take your time and be careful. Overpack to be safe and you'll be able to rest easier knowing you did all you could to successfully ship your guitar.