How to save WordPress Options as an array?

Have you tried…

 <input type="text" name="my_options[option1]" value="<?php echo $options['option1']; ?>" />
 <input type="text" name="my_options[option2]" value="<?php echo $options['option2']; ?>" />
 <input type="text" name="my_options[option3]" value="<?php echo $options['option3']; ?>" />?

I should say though (and maybe you have), that you should register your settings and perform necessary validation checks on the input – or if you really don’t want to use the Settings API, disregard it completely and ‘manually’ collect the form data, check the data, check nonces etc and add to the database.