I have many suggestions. I've moved around 20 times in my life, so we started getting VERY efficient and cheap! However, YMMV depending on the amount of stuff you have and need to move.
1) Get boxes from work or get big boxes from Costco (if you're a member). Ask others for empty boxes, either from their house or from their work. Don't buy them from anywhere if you can help it - but if you must, I would suggest buying them from a company like Uhaul.
2) Borrow a truck and some friends for the big stuff, and move everything that isn't big (bed, dresser, couch) on your own in your car. Stuff your car full - lower your backseat if you can. If you can borrow a bigger car or a van, stuff that full. I always liked to bring clothes and hang them right up, or a small shelf and put stuff right on it.
3) Depending on gas in your area, you may want to get a trailer from Uhaul instead of several trips in the car. Bonus points if you can borrow a trailer for free from a friend. Pack that sucker tight; no extra spaces left anywhere!
4) If you've got a good amount, then I'd suggest a mid-size Uhaul truck - they're VERY cost-efficient depending on how much you have. Buy only what you could stuff full - don't rent more truck than you really need. Packing tight keeps your stuff safe and free from shifting weights. Problem with these are that the cost of gas is prohibitive possibly - one tip might be to see if you could return the truck to a Uhaul store near your new place. Then, you won't spend the gas to return to the original rental place.
5) Use towels as packing cloths instead of bubble wrap and tape - towels will cushion dishes and breakables, and then can be washed and put in the closet instead of being thrown away like bubble wrap would be. Put scarves or socks in your shoes or pack them into purses to keep the shape of the shoes and purses. I personally wrapped an old comforter over my glass-top table to protect it - and kept the comforter as a spare once I got to my new house.
6) If you have luggage, pack shoes and clothes in the luggage OR pack smaller luggage into larger luggage. Create less for yourself to move by stacking things inside of other things. Large luggage is also good for dishes, smaller pictures and paintings, computer monitors (appropriately covered, of course).
Alright, that's all I can think of right now.