I am using
Joomla 1.5.26
JoomSEF 3.9.5,
BreezingForms 1.7.5 (free version)

To get Captcha to work in BreezingForms you must disable it in JoomSEF. Do this:
Components -> Artio JoomSEF -> Control Panel -> Extensions Management.
Find BreezingForms. Click the text in the column "Active Handler".
Click it until the text is "Not using SEF".
Now BreezingForms captcha works fine. See the attached image.