I'd say it depends whether simple anominity is all that is needed, or whether the sender also wishes to be immune from the forces of law and order, who may have special powers to compell ISPs and mail agents to disclose data logs under, say, the anti-terrorism laws.
If you just want to send a message to a friend as a joke then you can probably remain anonymous quite easily just by using webmail. You could also use an open smtp gateway, and spoof your source address.
But if your thinking of doing anything that would merit investigation by those with the above empowerments, you haven't got a chance. When you visit the webmail site, or hit the smtp gateway, your IP address would be recorded. Your ISP would then be able to identify you from their logfiles, even if the IP were dynamically allocated. I'm pretty sure the logs will be held for a very long time.
One thing that may allow you to cover your tracks a little bit would be to buy a payg mobile phone, refuse to tell the retailer who you are, and use that for sending the emails via a fake webmail account. Buy it and top up only with cash, of course, never a credit card. Even then, if they want to get you, and they have legal (or even military) powers, they always will.