Even without your own email hosting, Gmail kind of lets you do this by appending +whatever to your address before @gmail.com. Obviously this can be trivially detected and stripped but I suppose it is better than nothing. Multiple real Email addresses are definitely a best practice.
Like: myname+whatever@gmail.com?
Yep. I do this a lot. It occasionally doesn't work (eg: some sites don't think + is valid).
To be fair, I don't think it's made a huge difference in my life. In fact it's possibly been more of a negative than a positive.