The simplest way would be to modify the template and substitute the checkbox with a hidden input which is always set to 1. You need to edit the file /app/design/frontend/your_interface/your_theme/template/customer/form/register.phtml.
Remove this chunk of code:
<li>
<input type="checkbox" name="is_subscribed" title="<?php echo $this->__('Sign Up for Newsletter') ?>" value="1" id="is_subscribed" <?php if($this->getFormData()->getIsSubscribed()){ ?> checked="checked"<?php }elseif($this->getFormData()->getIsSubscribed == NULL){ ?> checked="checked"<?php }?> />
<label for="is_subscribed"><?php echo $this->__('Sign Up for Newsletter') ?></label>
</li>
And add your hidden input just after the other ones near the top of the form:
<input type="hidden" name="success_url" value="<?php echo $this->getSuccessUrl() ?>" />
<input type="hidden" name="error_url" value="<?php echo $this->getErrorUrl() ?>" />
<input type="hidden" name="is_subscribed" value="1" id="is_subscribed" />