Leavin' Time

Sometimes, to protect myself, I've kept a backpack or something...easily carried... and filled it with what I considered basic essentials. I grabbed one of the huge canvas hiking bags... perfect for camping, hiking, textbooks, whatever.
When going on the run, I like to generally have:
ID- yes, I don't generally go on the lam without it... I like to be able to check into hotels if I can.
Spare underwear- you never know when you'll need it. In lieu of pajamas, and not wanting to be completely bare on some of the cheap motels' muslin sheets, I'd have some basic pairs and a big T-shirt or sweatshirt, occasionally borrowed from or given by friends I affectionately referred to as "My Pet Monster".
MONEY. Cash is generally my favorite, although just in case a basic ATM card. It depends on if you feel you shouldn't be traced or not. ALWAYS HAVE CASH!
Ziplock bags. Quart to gallon sized. In these stow shampoos, soaps, and basic small food items- (in a separate bag)
A small bottle of Woolworth's laundry soap... the stuff you use to hand wash in cold water.
Hair brush, small curling iron if possible.
A box of tea bags. I like Bigelow Cinnamon stick. Find a clean cup and hot water, let steep, and it's a comfort.
Small container of non dairy creamer.
Spare throw blanket. A warm one.
Towels!
Wash clothes.
About a week's supply of clothing, clean dark jeans CAN be good if you absolutely cannot change.
Hair ties.
Bobby pins
A shopping list... no matter what, you need to shop sometimes. I can't pick up bread at a 7-11, but I can occasionally grab an essential doohicky, like batteries, or cigarettes if necessary. Back when I'd head up to motels up north in '03 and '08 for "Think it outs" I'd manage pretty well on "non perishables" I'd scrounged.
Something small that comforts you.
Deodorant.
Learn how to pack a lot of essentials into a tight space. I can surprise people with my toiletry bag.
Extra pair of light shoes.
CALL YOUR MOM OR SOMEONE YOU KNOW YOU CAN TRUST. Let them know you're ok. Now, if you are running from the law, not your own fear or from danger, then I am unable to help you. 
Oh, and never forget a well made belt. You might need to use it for more than holding up your drawers.
I also would hit the local reservation and pick up a carton of cigarettes. All of this, and more fit in a big hiking bag.
I made this stroll a few times while married, and engaged in a few trips east to get out of danger. Basically, I read, photograph scenery, think, eat where I can, find the natural foods stores, and attempt to just forget the danger for a while. I've also done homework and visited trustworthy friends. Above all, get out and get help. If you are in danger, do not embrace it. Walk away.