Please list some web apps that allows you either to
As always with such lists: one service per answer.
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You could just use plus-addressing in Gmail. Basically you just pop a + after the username part of your email (email@example.com will go to the mailbox for firstname.lastname@example.org, but will allow easy filtering). They're sort of temporary and not really anonymous, but they would allow you to filter out based on rules etc. Big downside is that clever spammers would just remove the + to get around your cunning filters.
Another option is to use a Google Apps account with your own domain name (so you can have unlimited email addresses). Just add a temporary alias for your normal user - allow the email you want to come in, then remove the alias... A lot more temporary than my other answer and a bit more anonymous. Still not perfect...
OtherInbox's DEFENDER offering has this functionality. You sign up and get USERNAME.otherinbox.com and USERNAME.oib.com subdomains (or you can use your own domain) and it sorts/filters anything sent to that domain.
I've been using the service for over 2 years now and have been pretty happy with it. They started off focusing on providing a web mail client experience but have since started focusing more on tapping into existing webmail accounts (gmail, yahoo) and sorting messages that come in based on type.
Make sure to sign up using the DEFENDER link at the bottom of the page.
I use the Sxipper plug-in for Firefox, and it includes a temporary e-mail redirection service.
10MinuteMail may be what you are looking for.
I prefer Temp Alias. It allows you to set how many days the email will be active for, but another unique feature is you can set how many email's it is alive for. So for example you could say after this email has been emailed 3 times, destroy it.
For a temporary address for receiving e-mail, you can use Yopmail. Just don't forget to delete your message after you have read them since everyone can read the messages.
Jetable will forward to the address you specify for one hour/day/week/month.