Not every move is the same, some easier than others and knowing what items to buy beforehand prevents an inevitable stressful situation from becoming a full-blown disaster. These four items cover 99% of moves so keep these in mind when planning the next move.
Cardboard Boxes
Unless you live in a cardboard box yourself then chances are you have items that need to be safely transported from A to B in the most cost effective manner. A variety of boxes is a sensible option since they come in a variety of sizes, shapes, and strengths to give you peace of mind while your items are in transit. Specialized boxes and partitions can be used but most items can be safely transported with the following and a bit of pre-planning:

Bubble, Foam or Paper Wrap/Kraft Rolls
Simply wrapping your valuable items in any type of protective wrap greatly reduces the risk of something breaking. The usual suspects are bubble, foam or wrapping paper. Would you want to drive on the highway without airbags? Probably not, so why would you risk the same with any fragile priceless items. Prevention is worth a pound of cure.

Carton/Packing Tape
If you enjoy hauling tons of rope and having blisters from tying knots all day then feel free to skip to the next section, if not then you might want to grab yourself some rolls of packing/carton tape. Having a roll of tape at your disposal can work wonders sealing boxes, securing loose items or even adding an extra level of protection. Custom printed tapes that say “FRAGILE” or “Do Not Shake” are readily available and help identify items during a hectic move.

Permanent Markers and Utility Knife
Labeling each box not only reduces the number of accidents (i.e. stacking a heavy book box on a fragile box) but also keeps inventory of where things are. Making a list of items as they are packed and labeling them once sealed with packing tape is as common of a procedure as making sure your moving truck has gas before you head out. The importance of a quality knife is often left out of the move but can make all the difference while packing and unpacking. A set of dull keys, steak knife or open pair of scissors simply doesn’t cut it, pun intended when precision, speed, functionality and safety are needed to move things and people along.
There are many other items that could be used (e.g. garbage bags, file boxes, dollies) but 99% of moves can be done with those four items and a little bit of prep on moving. The alternative for some are moving kits which are value priced and are super convenient. The real challenge is finding reliable people to make your move the stuff of dreams and not nightmares.

Good luck, have fun and remember to lift with your legs and not your back!