do I have to print online purchased tickets?

Maria, in case no one is able to give you a comprehensive answer:

• I saw many young Spaniards showing drivers confirmations on their smartphones before boarding inter-city buses. I just went to the bus station a day or so ahead of time and bought a ticket, usually via a vending machine. When the bus station was in an awkward location (Madrid's are scattered all over the place), I just showed up and took my chances since I was going to destinations with frequent buses. I don't necessarily recommend that plan, especially for someone on a short trip.

• In Barcelona I bought my tickets for the scheduled-in-advance sights at the Pl. Catalunya ticket office, except for the ticket to the Palau de la Musica Catalana, which my sister-in-law took care of online far in advance. The T.O. had a convenience charge of 1 euro per ticket in 2016, but I was happy to pay it. The T.O. handled regular tickets for La Sagrada Familia but not the tower-climb tickets. Although buying a day or so ahead may get you a ticket, you may not get one for the time you want at the many high-traffic Barcelona sights, which in my experience are: La Sagrada Familia, Parc Guell, Palau de la Musica Catalana (tour required), Casa Batllo, Casa Mila/La Pedrera, Picasso Museum (an absolute madhouse despite being ticketed) and Camp Nou. Camp Nou (soccer) may be a place that has to be booked way in advance; I don't know because I didn't go there.

• It has been reported here that a few of the Barcelona sights sell more-expensive wildcard tickets that do not tie you to a specific entry time.

I would. What if your phone battery dies or you lose your phone?

I always print out tickets just in case. As mentioned, there could be battery problems, or some other phone malfunction. And that goes for boarding passes as well as admissions to museums, theaters, etc. While I can't say that I've had a problem with the phone versions, I guess I'm enough of a Luddite to prefer having the backup of a paper copy!

In Europe it varies from place to place. The websites of each venue should let you know their policy.

Thanks for the varied responses and experiences. I do charge my phone every day and know my battery levels. Stays well locked away until needed. Not attached to my hip. I rarely worry about losing it despite the pickpocket stories. I plan to stay in apartments, so printers not guaranteed. Usually I print too, but do use e tickets for flights and trains, so transitioning.
If I commit to Barcelona before departure, I might buy and print Sagrada Familia before I go. Rest are based on what is available. I plan a lot ahead, but cannot bring myself to tie everday into a rigid schedule. I take a certain level of risk, or leave it to kismet.
Thanks for the tip about some places requiring paper. Those might be the ones I consider the TA for then. That was a good tip, acraven. Thanks. I don't use TAs enough.
Thanks all.

We printed copies also. Most of the tjme it works via the phone, but it is peace of mind to have paper just in case.

I was in line at Palma airport to board and my phone decided not to open my electronic boarding pass. A mad scramble ensued to get a printed one at the gate.

To clarify: The place I got my Barcelona tickets was the official tourist office located beneath Pl. Catalunya. I believe Enric has mentioned another place or places where such tickets can be obtained, but I don't remember the details.

I printed everything and found it to be quite useful. Plan ahead. Still a lot of visitors in Spain in October.