How can I check if file has been downloaded in ansible

Unless you have a reason to use wget why not use get_url module. It will check if the file needs to be downloaded.

---
- hosts        : all
  gather_facts : no
  tasks:
   - get_url:
       url="http://mirror.mel.bkb.net.au/pub/apache/lucene/solr/4.7.0/solr-4.7.0.zip"
       dest="{{project_root}}/solr-4.7.0.zip"

NOTE: If you put the directory and not the full path in the dest ansible will still download the file to a temporary dir but do an md5 check to decide whether to copy to the dest dir.

And if you need to save state of download you can use:

---
- hosts        : all
  gather_facts : no
  tasks:
   - get_url:
       url="http://mirror.mel.bkb.net.au/pub/apache/lucene/solr/4.7.0/solr-4.7.0.zip"
       dest="{{project_root}}/solr-4.7.0.zip"
     register: get_solr

   - debug: 
       msg="solr was downloaded"
     when: get_solr|changed

Many modules are already aware of the result and will be skipped if its already there, like file or geturl. Others like command have a creates option, which will skip this command if that file already exists (or doesn't exist, if you use the removes option).

So you should first check the available modules, if they are smart enough already. If not: I recommend the stats module. Advantage over the other solution: No "red errors but ignored" in the output.

- name: Check MySQL data directory existence
  stat: path=/var/lib/mysql-slave
  register: mysql_slave_data_dir

- name: Stop MySQL master to copy data directory
  service: name=mysql state=stopped
  sudo: yes 
  when: not mysql_slave_data_dir.stat.exists

There are at least two options here.

You can register a variable if the file exists, then use a when condition to execute the command on the condition that the file doesn't already exist:

- command: /usr/bin/test -e {{project_root}}/solr/solr-4.7.0.zip
  register: solr_zip
  ignore_errors: True
- name: Download Solr
  shell: chdir={{project_root}}/solr /usr/bin/wget http://mirror.mel.bkb.net.au/pub/apache/lucene/solr/4.7.0/solr-4.7.0.zip
  when: solr_zip|failed

You could also use the commands module with the creates option:

- name: Download Solr
  command: /usr/bin/wget http://mirror.mel.bkb.net.au/pub/apache/lucene/solr/4.7.0/solr-4.7.0.zip chdir={{project_root}}/solr  creates={{project_root}}/solr/solr-4.7.0.zip

Note: this answer covers general question of "How can i check the file existence in ansible", not a specific case of downloading file.

The problems with the previous answers using "command" or "shell" actions is that they won't work in --check mode. Actually, first action will be skipped, and next will error out on "when: solr_exists.rc != 0" condition (due to variable not being defined).

Since Ansible 1.3, there's more direct way to check for file existance - using "stat" module. It of course also works well as "local_action" to check a local file existence:

- local_action: stat path={{secrets_dir}}/secrets.yml
  register: secrets_exist

- fail: msg="Production credentials not found"
  when: secrets_exist.stat.exists == False