It would be way too easy to answer this question with: “Whoever pays your bills.” And, honestly, I don’t think you can be a very successful web designer if you’re only driven by what the person paying you tells you to do.
Then again, that doesn’t mean you should swing to the exact opposite end and say that you only serve the end user.
When you take an extreme view or approach to this, you’re bound to leave someone or something important out. Everyone along the chain of command — your boss (if you work at an agency), your client, and their customers — matters.
So, what I’d suggest you do instead is approach the idea of who you really work for the way you would Maslow’s Hierarchy of Needs.
Establishing Your Own Hierarchy of Needs
Who do web designers really work for? I think the true answer to this question is: “Everyone.