Trees are a renewable resource*, i.e. if you cut one down, you can simply plant a new one.  Sure, it has to grow to the right size before it can be cut down and used again, but the principle is there.  That's why I don't feel incredibly bad about wasting paper.  It's not that I'm out to waste as much as possible, but I'm not overly concerned about the prospect of running out of trees.  Plus, paper is biodegradable.  So while it may sit in a landfill for a little while (if it's not recycled), it'll eventually break down into some pretty simple components and disappear into nothingness. 

That being said, forests aren't a renewable resource, and that's where the problem lies.  If I cut down a tree, I can plant a new one.  If I cut down a forest, I kill all the inhabitants and destroy the ecosystem, and that's not good for anybody.  So while I'm not concerned about using trees for paper and wood, I am concerned about where those trees come from and how many are left in place.  However, this is all outside my sphere of influence, so I guess I can't really do much by being concerned. 

*I generally don't like linking to user-contributed answer sites, but this one was written intelligently and concisely.