Here are some possibilities depending on the context:
* For sticks or logs: a pile, a stack, a heap
* For papers: a stack, a bundle (this is the most common), a sheaf, a pile
* For clothes: a heap, a pile, a bundle (this is common), a wad, a stack
* For money: a wad, a stack, a bundle, a roll, a heap
Ultimately, the best collective noun depends on the specific context and what you want to emphasize.