For hanging packs, you can use vines. Find a vine you than can bend almost double (the shape of those ribbon campaign ribbons) without it breaking. You can use those as is, until they dry out. If you need more weight, you can braid them.
If you can't find vines, you can use new green bark off of smaller plants. If you can peel at least 12" of bark, you can braid it. Make sure that you pick a bark that does not easily snap when pulled on. Obviously peeling bark is really harmful to the plants so don't do this for trivial needs.
For small ties, you can braid longer grasses. This will work fairly well for anything that does not need to hold a lot of weight, for example, f you just need to tie something closed. We have used this to tie on bandages in a pinch before. Again, as with vines, if you can't bend it in a small loop without a crack, it will not make good cordage.
There are a lot of braids for rope. I've always used the simple three strand braid shown here. http://www.youtube.com/watch?v=F_hHhtQGNus.
Braiding multiple strands to make a rope of longer length out of shorter strands is pretty tricky. I wouldn't recommend trying it unless you practice a lot at home first.