1. Stay organized by keeping lists. I have a cleaning task list, packing-by-room list and, perhaps most important, a what-in-which-box list. Since I'm only packing for a college apartment, I have a lot of random small things that just end up in a larger box: cleaning supplies, laundry soap, lightbulbs, etc. I also advise labeling your boxes with a marker on every side. It's always a pain to open a box only to find it isn't the box you wanted. Which brings me to...
3. Keep boxes that come with your purchases. The box for my blender had so much leftover space inside, so in that I packed not only my blender, but also measuring cups and spoons, an ice cream scoop and my large chef knife. All these odds-and-ends kitchen items are now in one place and not taking up space in a separate box. The same happened with my assorted baking pan box, in which I packed three extra pans that didn't come with the set. Packing win!
6. Be realistic about trash. Junk is junk. I like to go through my notes at the end of the semester and throw out whatever isn't worth keeping. I also use this practice for clothes: if I haven't worn it (or refashioned it into something else, as I like to say I'll "one day" do) in six months (with an exception for season-specific items, like scarves), it needs to be tossed or donated. Being honest with yourself about what you really need will reduce the amount of stuff you need to pack and give you a fresh start for your new place.
These tips may seem pretty obvious and standard, but they've really helped me stay organized throughout this move. Have any other packing suggestions? Let me know in the comments below!