I was having problems in contact form 7 uploading files and not the form not being able to generate CAPTCHA images (despite permissions being set correctly).
If you are having these problems, take a look at your site's error log. For me the problem was that PHP safe_mode was enabled:
SAFE MODE Restriction in effect. The script whose uid is 10062 is not allowed to access /var/www/vhosts/site.com/httpdocs/wp-content/uploads/wpcf7_captcha owned by uid 48 in /var/www/vhosts/site.com/httpdocs/wp-content/plugins/really-simple-captcha/really-simple-captcha.php on line 111, referer: http://site.com/upload-form/
Get your webhost to give you access to the error log and take a look - it may well be that your PHP is operating in safe mode too.