Even after moving from one side of the country and back with a houseful of furniture, two cats, and a baby I must admit that I'm probably more qualified to give tips on what not to do when moving long distances, but here are a few things I've learned from the experiences based on my failures and the occasional success.
Reconsider Movers: When we moved from New York City to LA we hired movers who took 4 weeks to transport our stuff, were impossible to get ahold of and cost an arm and a leg, even before gas prices shot through the roof. When we moved back to the east coast, we used ABF, a shipping service that will drop off a pod or truck at your house for you to pack up yourself. However, since parking in front of our place was hard to come by, we split the difference and hired movers to transport our stuff from our house to the ABF shipping warehouse. Not only did we save a ton of money that way, but much of the heavy lifting was left to professionals, plus we could easily track our stuff (which arrived in only one week) online.
Pack Well: The further you are moving, the more bumps in the road your things will encounter along the way and it's virtually impossible to avoid some damage. Many moving companies will provide blankets and other packing materials for exorbitant prices, so stock up and package everything as well as you can yourself. Uline and U-Haul sell tons of supplies, including odd-shaped boxes, and craigslist is also a great resource for used moving supplies.
Purge (Thoughtfully): While it's always tempting to get rid of lots of things before a long distance move since you usually pay based on how much stuff you have, we found that the best thing to do is weigh the value (both sentimental and monetary) of each piece of furniture against the costs and effort to ship it. The first time we moved, we brought way too many pieces of IKEA furniture that were more expensive to ship than they cost originally, but the second time we found ourselves getting rid of some things that probably would have been worth it for us to keep.
Drive Your Car: Shipping a car can be a horrendous nightmare which usually involves reserving a spot for your vehicle months in advance and not being sure when it will actually be transported. If it's possible for you to drive, I highly recommend it. If you do ship, use a company that doesn't require a deposit.
Be Emotionally Prepared: This may sound gooey, but even if you are moving somewhere with lots of friends and family nearby, it's a huge life change so give yourself time to settle in. Moving across town is hard enough, let alone moving to a new state or part of the country where you need to figure out pretty much everything all over again.