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.
Ranked in these QuestionsQuestion Ranking
Pro Anonymous replies
You can reply to emails via 33mail without disclosing your real email address.
Pro Permanent email aliases
Email aliases aren't temporary, but they can be blocked.
Pro It's been around a while so it ain't going anywhere
33Mail started in 2011 and has been growing steadily since then, forwarding over 1m emails per month as of 2018.
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 firstname.lastname@example.org. That's with the free plan, but with the paid plan you can use your own domain name.
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.