If you're using a payment gateway that has the users enter their credit card number on your site, you'll need an SSL certificate installed on your site and you'll have to enable HTTPS on your site to protect your visitors' information.
Official WooThemes.com payment gateways that should use an SSL certificate will not work without one. This is a good thing, because you can't set it up wrong and then be liable for stolen credit card numbers.
Note
There are some payment gateways that look like you're entering a credit card number on your site, but they might be using technology to embed a secure page within your site. If you're using a WooThemes plugin, don't worry about it. All of those plugins have been audited and are secure. If they require an SSL certificate, they will be clearly documented.
If you're using a plugin from a third party, it's worth checking with the developers to make sure everything is secure.