Why is multiple hashing not a good idea?

There are plenty of questions on this site about hashing passwords. However, none of them quite cover this topic. One of those links covers using multiple different hash algorithms; one covers general hashing, and the other covers how passwords should be transferred. However, I want to know what the security implications of using one hash function multiple times.

I came across an article a while ago saying that this is not a good idea. However, I want some definitive answers. So, what are the security implications, good or bad, of using a hash system like this:

hash(hash(hash(password) + salt) + pepper)

In other words, hashing the password, then hashing the hash of the password with the salt, then hashing this hash with the pepper.