The problem isn't sending anonymous mail so much as hoping that the mail will get there. Old mail systems were trusting, so you could easily send mail pretending to be from anyone and it would be very hard to trace backward.
Nowadays though, with all the spammers doing what they do, mail servers are less trusting and have security in place to block mail claiming to be from hosts that don't have the authority to claim to be the origin of those emails.
For example, if Kathrine has a Gmail address, she can send mail using Google's mail servers to Sadaf who's using AOL. However if Greg, who doesn't have a Gmail account tries to send mail to Sadaf pretending that he's Kathrine (or anyone @gmail.com for that matter) Gmail will reject it.
You can go a step further to setup your own mail server with its own domain (myawesomemailserver.com) and *then* create an account (firstname.lastname@example.org) and put everyone online for everyone to see and then send mail, but at that point the mail is traceable to the owner of the domain (you) so it's not very annoymous.
If you want to send an email to someone anonymously, the best option is always just to setup a free account with a web service (like gmail, yahoo, etc.) and use that. You can even send the mail from an internet cafe, or a "borrowed" wireless connection if you must.
Just don't do anything evil. They'll find you, and it'll hurt.