ha, you'll be bound to forget something, and make a couple runs to Bed Bath and Beyond.
make sure you have enough lighting...hmmm...fire extinguisher, if one doesn't come with the apartment. *looks around room* cleaning supplies, like vacuum, windex, rags, etc. Dishwasher soap if you have a dishwasher. um...ha, ant poison! We're having a major infestation right now...
That's all I can think of.
It's crazy to live on your own for the first time! Do you have a roomate, or are you all by yourself?