No, you do not need anything other than the printed e-ticket and your passport (which should often be valid for at least six months beyond your travel date to satisfy immigration rules). But there are documents you may have to have. Typically, depending on your passport and destination, to enter a country you may need to apply for a visa before flying. But in any case, this is up to you to figure that, this is not the airline's job.
If you're flying domestically you can board without a passport in most places (still, some identity document may be asked), but a passport will work also.
Finally, printing the e-ticket is not completely necessary in most cases, but it is a good idea for a few reasons, such as reminding yourself of your flight times if your phone battery dies, and convincing immigration officers that you will return home by showing them your return ticket (many immigration areas do not have Wi-Fi).