1) Food. Pack for a week or two in advance for your dog/cat/rabbits/guineas/etc. size. If you can fit in your entire bag of food, go for it. You're better off having extra.
2) Water. Fill up jugs with water or bring water bottles.
3) Leashes, Harnesses, Collars. If you're in a rural area and don't have a collar for your animal -- there is other options until you can find one. The orange stuff hikers use to mark trails is a good option, and you can write on it for ID purposes. However, remember that plastic and other materials will melt! Pick wisely, and pick up a leash or collar when safe.
4) Kennels, Crates & Carriers. Not only is it go to have with you, but in the event you have to leave your animal at a boarding facility or with a relative, it will help to have a place that smells like you and your home.
5) POOP BAGS. It's already a shitty situation, dont make it shittier. wink emoticon
6) Toys, Bed/Blankets & Dishes.
7) Extra Equpiment you might have for behavioural issue (ie. Head Harness, Muzzle, etc). You might not know where you're going to end up, and one of the places might just have a bunch of other animals
8) VET RECORDS AND OWNERSHIP PAPERS.
9) Pet medications!
10) If dropping off at the SPCA or boarding facilities, please be sure to inform staff of any and all habits and quirks. Tell them if your dog or cat is aggressive, timid, plays well with others, does not play well with others, shy of women or shy of men -- list goes on. This is important information so they can house your animal appropriately and make sure thay every animal in their care is safe and sound. smile emoticon
Will add more to list as time goes on smile emoticon Suggestions are welcome!