We have a service where we literally give away free money.
Naturally said service is ripe for abuse. To defend against this we do the following:
log
Re: signing up for new email accounts...
A user doesn't even need to do that. Please feel free to send your mail to brian_s@mailinator.com, or feydr.asks.a.question@spamherelots.com, or stackoverflow@safetymail.info, or my_arbitrary_username@zippymail.info. I haven't registered any of those email addresses, but all of them will work.
Those domains are owned by ManyBrain, and they (and probably others as well) set the domain to accept any email user. ManyBrain in particular then makes the inboxes for those emails publicly accessible without any registration (stripping everything by text from the email and deleting old mail). Check it out: admin@mailinator.com's email inbox!
Others have mentioned ways to try and keep user identities unique. This is just one more reason to not trust email addresses.