Summary:
If you have a custom domain, this gist will show you how to create unique, on-demand, "disposable" email addresses such as "from.twitter@mydomain.com" or "from.amazon@mydomain.com" without prior setup. There is also an alternative method listed, if you don't have a custom domain.

Origin
GMail, and other mail services, offer the ability to create unique email addresses on-demand, without prior setup, via a technique called "plus addressing." If you're wary of revealing your actual email address, plus addressing can create a unique variation specific to share.

What is plus addressing?
Imagine your GMail address is clarkgriswold@gmail.com. You may be required to submit your email address to subscribe to a newsletter or register for a new web site, but you're afraid of receiving spam, or you want to see if they share your address with 3rd parties. Instead of using clarkgriswold@gmail.com directly, you can use clarkgriswold+something@gmail.com. Now you have a unique address that you can later block or search for, and trace back to this specific sign-up. Of course, you can use anything after the + sign, you don't have to set up these extra addresses ahead of time, and they all get delivered to the same inbox. So you could create clarkgriswold+twitter@gmail.com, clarkgriswold+facebook@gmail.com, clarkgriswold+reddit@gmail.com, clarkgriswold+whatsapp@gmail.com, etc. Now, you can see exactly who these services share your email address, because anytime you receive an email to clarkgriswold+facebook@gmail.com, you know how that company got your email address. You can also set up filters to automatically delete, or forward, or categorize, any email with a specific +suffix.

The biggest problem with plus addressing is that it is trivial to eliminate the plus suffix and obtain the original address. Anyone who is aware that GMail offers plus addressing can just strip out the plus sign and suffix before sharing or using your email address.

Another problem, if you use your own domain for email, is that plus addresing does not exist, since you're on your own mail server and not on the GMail platform.

So, what to do? Here's a simple-to-set-up alternative for custom domains that goes further than plus addressing to maintain anonymity. As mentioned in the summary, you can create "from.anything@customdomain.com".

The following steps are for use on CPanel, although the same concept should work on most mail server software:
Go to Global Email Filters
Give the filter a name
Set the following rules: "To" "matches regex"
Use this regex - make sure you have all the slashes and dots, don't include the quotes: "from[\._-]+[\w\d]+\@yourdomain\.com"
(yourdomain should be substituted with your domain name)
Action: Redirect to Email, then enter your primary email address.
Save

Now you have created an anonymous mask in front of your actual email address. So you can create from.espn@yourdomain.com and have it delivered to your primary email address. The regex gives you flexibility to also use a dash (-) or underscore (_) instead of the dot. So from-espn and from_espn will both work as well. Note that unlike the GMail plus addressing scheme, your original email address cannot be reverse-engineered. You are exposing your domain name, so it is not totally anonymous, especially if the domain is registered to you, but the specific email address you use is hidden and protected.

Note you can create a second filter with a slight varition, if you have multiple email addresses. For example, by changing "from" to "source" (or something else) in the regex, you can create additional filters with distinct Redirect targets. At the same time, if you have multiple domains, you can have multiple filters by changing the domain in the regex.

Alternative method
33mail is the best "disposable email" service I've found. Unlike Mailinator, messages get delivered to your inbox. However, you do need to sign up for an account (which is free) and the forwarded messages have ads inserted by 33mail. But it is fast, flexible, and gives you statistics like exactly how many emails were sent to a specific address. Paid accounts can also reply to an email anonymously, which neither plus addressing nor my regex method can allow. Free accounts can do this too, but limited to just once per month.