In order to remove the discount code block you have to open the checkout.xml file which is located in /app/design/frontend/default/[your_theme]/layout/checkout.xml.
If there is no such file, copy it from /app/design/frontend/base/default/layout/checkout.xml to your theme and…
Remove discount code block
Open the file and delete the following code:
<block type=”checkout/cart_coupon” name=”checkout.cart.coupon” as=”coupon” template=”checkout/cart/coupon.phtml”/>
If you want to delete the ESTIMATE SHIPPING AND TAX block, remove the following code from the same file. The code should be just after the previeous line.
That’s all. Do not forget to refresh the cache.
By the way, “Discount code” is very useful for promotion, so it depends on you.