Tweetake.com works well for downloading your Twitter posts as a .cvs file for backup but it requires your user name/password.
You can follow the sequence below to avoid problems with any site requiring your Twitter password:
1. Change your Twitter password.
2. Log in the 3rd party website.
3. Get the data you want.
4. Change your Twitter password back to the original one.
Image source: Twitter.com logo, computer image is public domain.