I have publishing site where users can add their own pages to some libraries. I have problem with permissions when user creates new page. Here's how I set permissions:

all users are added to members group (by default they can view pages)
members group has view permissions also for master pages library
For site where users can add pages I set the following permissions on pages library
users can add view pages
users can add pages
When user adds new page then he/she gets automatically edit permissions for this page. So users can edit only their own pages.

I found out that add permission is not enough - when user creates page then he/she gets access denied error. The minun that doesn't cause problems is approver permission to pages library (of course, now users can do everything on pages library they ever want to do). Is there any way to avoid making users as approvers?

They only need view and add permissions for page library and view and edit permissions for pages they added. They cannot do anything more. Approving and denying of pages is administrators job.