Recs.
Updated
33Mail doesn't just give you an email alias, it gives you an email domain under which you can create as many aliases as you need.
These aliases will instantly forward to your main email address, and you can even reply to them anonymously without revealing your real address.
The aliases aren't time-limited, so you can use them with any website - only deleting them if the website starts to send you email you don't want.
There is a generous free tier, but for $1/month you can upgrade so that you can use your own domain name, along with various other benefits.
33Mail has been around since 2011, so it's not a "here today, gone tomorrow" startup.
Specs
Pros
Pro Your own email domain
With 33Mail you get your own domain, like dogbert.33mail.com - and you can create as many aliases as you want under this, such as slant@dogbert.33mail.com. That's with the free plan, but with the paid plan you can use your own domain name.
Cons
Con Terrible customer service, no way to stop charges if you sign up for premium
After 1 year they auto-charged for the 2nd year. There is NOWHERE on their site to remove your credit card info. You can write to them them in advance several times to please stop your premium service, but they will charge you anyway. Terrible customer service.