Can I show a promo banner like “Spend $X more to get free shipping” in magento?

Yes, that’s possible with this extension. Say, you provide free shipping on orders $100 and up. Then you can set the following Cart Conditions on the Banner page:

This way if a customer has added products to his shopping cart, and their subtotal is less than $100, the promo banner will be shown.

Banners work well with any 'Buy X Get Y Free' Magento promotions, not only shipping.