When I purchase flights with an online travel agent, is there an "e-ticket" I must print out?

By it's very name, an "Electronic Ticket", or an "E-ticket" is not a physical item - it's just an entry in a computer system.

As a result, you do not need to physically present any specific document at time of check-in in order to get your boarding pass. So technically, no, you do not need to print anything out at all.

However there are a few places where having a printout will be very beneficial (and in some cases, required by law). The first of these is if there is a problem! There is always the potential that something will go wrong, either with your booking or with the flights, and having a printed copy with the exact details of your flight (including confirmation number and e-ticket number) can certainly help in these cases. This is especially true if your booking includes multiple airlines, as the first airline may not be able to see all of the details of your later flights on their computer if they are on a different airline.

The second is when you're traveling internationally. Many countries will require you to be able to show a return or onward "ticket" in order to get through immigration, and in some cases the airline will also need to see the details of such ticket before you board the outbound flight (if the flights are booked on a different ticket). Whilst a printed itinerary from your travel agency/website/etc may be enough here, it's always better to have a printout of the e-ticket itself.

As far as what to print, there's a few options. What the travel website has given you is probably OK - just make sure that it's got the "Confirmation Number" or "Record Locator Number" on it (normally this is a 5-6 character alpha/numeric string, like "Y7EMM4") AND your E-ticket number (normally a 13-14 digit number). You can often also find an option on the website to print out your e-ticket and/or your receipt which will normally contain the relevant details.

If you can't find somewhere on the booking website that will give you a clean copy to print, try the airlines website. You should be able to lookup the booking on their website using your Confirmation Number, and they will normally have an option to view/print your booking details, which will normally include the e-ticket number. If your trip covers multiple airlines, you may need to do this step on each of their websites to get all of the details.

On two different occasions I have had issues flying Lufthansa on an Air Canada ticket - their systems don't work together as well as they should - which were solved only by a tremendous amount of typing by the checkin agent. A vital part of this typing was my ticket number. Since I had nothing printed, I just opened the confirmation email on my laptop and handed it across the counter to the agent. If you don't intend to bring a laptop with you, then print the email. Sure, it has extraneous junk in it, but if you need it, you need it.

My laptops always have plenty of battery when I arrive at the airport, and I keep my emails locally so I can read them even without internet access. Important emails like hotel, flight, and car reservations are duplicated on my phone, which also has plenty of battery when I arrive. If you're traveling for leisure you will probably find a few pages of paper easier to deal with than two fully charged electronic things along with remembering to move stuff from the cloud to somewhere on your hard drive.

As others have said, modern e-tickets typically don't require you to take any paperwork to the airport beyond your passport.

However, I have once or twice (for example, in Mumbai) been asked for ticket paperwork to gain entry to the airport or check-in area (for 'security' reasons). In one case, my travelling companions, who hadn't printed their details out, had to go and find a printing kiosk for exactly this reason, at the last minute, at great expense and stress.

So whilst it's not necessary, it's always wise to print out the details of your intended itinerary, e-ticket number, and reservation code anyway, just to be on the safe side - or at least have them noted somewhere accessible electronically.