If you’re moving, you’re going to spend money; there’s really no way around it. It is, like many things in life, an investment. If you plan on handling most of the process yourself, part of that investment is time as well. The likelihood that you happen to have all the equipment you need just lying around is scarce (unless you are yourself a professional mover), so you’ll probably find yourself having to rent a few items to make this whole thing doable and efficient.

"This beaujolais is almost as well-balanced as my handtruck."
In all of these cases, use the resources you have available to you before you set out to spend your cash. If you have friends that have moved themselves before or used a particular rental company, ask their advice so you don’t end up paying for things you don’t need. You might even know people that have this equipment already. Just ask; it’s not something that comes up naturally at dinner parties (do people still have those?).
Depending on the size of your move, you may need a truck or van to transport all of your stuff. If it’s just a move to a dorm (not to belittle that headache of a process; I’ve done it a few times myself), you might be able to get away with using vehicles you have. If not, a van is probably sufficient, especially if you aren’t bringing any large pieces of furniture. Check out the different sizes of vehicles they have at the rental place.
In the case of using a moving truck (we’ll assume you’re moving into a new home from now on), get something 10-15% bigger than the actual volume of your stuff. Talk to the rental company about how many rooms you have in your house and the types of appliances you’ll be taking with you, so they can help you pick the right-sized vehicle.
Dollies or handtrucks are vital if you’re going to be taking a refrigerator or any other large appliance along with you. Make sure you find out exactly what the dolly is built for, poundage-wise, and try to find one with straps, especially if you’ll be moving these behemoths down stairs. You’ll also find that dollies make transporting boxes a lot easier. You can just stack a bunch on there and wheel it away. It’s very satisfying.
You’ll also need some blankets. If you like your furniture to look nice, that is. If you have a surplus of them, and you don’t mind them getting dusty and beaten-up, by all means use throw those over your bureaus, etc. Just remember that moving blankets are special for a reason: they’re thick, tough, and big.
All of these items will be readily available at a rental company. So, go to a few; compare prices. Last, but not least, don’t let pride result in injury. Get your friends to come help. Buy bagels and coffee for everyone: they’ll show up.