For this assignment, we learned about accepting payments online. This can be as simple as putting a PayPal donations button on your site, or as comprehensive as an end-to-end solution that handles every aspect of ecommerce on your site.
Since my site is simple and I'm not selling anything, I opted for the PayPal donations button (don't be shy!). But for people in need of more robust solutions, there are plenty of options available. These options may or may not involve PayPal, although a wide variety of retailers use it. Which solution is best depends on what you're selling and what features you're looking for.
If you're selling primarily software or other downloadable content, you might consider MyCommerce. They specialize in the particular issues surrounding downloadable content, such as secure downloads and license codes. Shopify offers complete ecommerce solutions including setting up the shop pages and even integrating with fulfillment providers to make shipping easier.
I wouldn't recommend it as a sole payment option, but I must confess my fascination with Bitcoin. I love it when somebody tries a totally new way of doing things. Bitcoin is an alternative, digital-only currency that isn't tied to any government central bank. There are reputable companies that accept payments in Bitcoin, like Wordpress and domain registrar Namecheap. Remember MyCommerce from the previous paragraph? They also accept Bitcoin.
So, in a nutshell, there are a ton of options out there for handling ecommerce on your site. If you're going to have transactions with any real frequency, it's probably worth your time to research which provider is the best option for your particular needs. Chances are there are some who specialize in businesses like yours.