Ansible - Mode 755 for directories and 644 for files recursively

The Ansible file/copy modules don't give you the granularity of specifying permissions based on file type so you'd most likely need to do this manually by doing something along these lines:

- name: Ensure directories are 0755
  command: find {{ path }} -type d -exec chmod -c 0755 {} \;
  register: chmod_result
  changed_when: "chmod_result.stdout != \"\""

- name: Ensure files are 0644
  command: find {{ path }} -type f -exec chmod -c 0644 {} \;
  register: chmod_result
  changed_when: "chmod_result.stdout != \"\""

These would have the effect of recursing through {{ path }} and changing the permissions of every file or directory to the specified permissions.

Since version 1.8, Ansible supports symbolic modes. Thus, the following would perform the task you want:

- name: Make my directory tree readable
  file:
    path: dir
    mode: u=rwX,g=rX,o=rX
    recurse: yes

Because X (instead of x) only applies to directories or files with at least one x bit set.