Which Barcelona sites need advance tickets?

I haven’t been to Barcelona yet, but am going in September. I can only tell you, through my extensive research, that it is best to get tickets on line to any and all of those sites that are most important to you. You can purchase them on line. I would suggest doing so ahead so you do not waste precious time waiting in lines.

I know- it kind of messes up a spontaneous day- but if you really want to see these these you can plan for a timed entry entrance to each and avoid spending many (possible) hours in line.

Perhaps someone who has been there recently could give better advice, but this is what I have seen through my recent research. I have purchased on line tickets to each and also the Palau de La Musica which you didn’t mention but sounds to be amazing.
Happy travels!
Lisa

All that you listed need advance tickets so you don't get hung up in a very long ticket-purchase line. Any of them could sell out before the end of the day, too, even if there were tickets available at the beginning of the day.

I haven't bought tickets to any of those places since 2016 and am confident the ticket situation is tighter this year. (That's certainly true in Rome.) As of 2016, the local tourist office advised me that the very early tickets tended to sell out first. It was suggested that I buy my first time-slot ticket to La Sagrada Familia at least two days ahead of time, whereas tickets for later in the day could probably safely be purchased just the day before. I wouldn't push my luck to that degree now, unless I was absolutely prepared to miss out on the sight.

Two others that need early attention if you should decide to see them are Casa Batllo and possibly the Palau de la Musica Catalana. The English language tours at the Palau sell out sometimes; I don't know whether there's an alternative for English-speakers; an audio guide might now be an option.

The number of tickets (all of them timed as well as dated) that need to be pre-purchased in Barcelona is a big pain for tourists, so I'll mention some places where I think you can be sure of not running into a significantly long ticket line: the Sant Pau modernista site, the MNAC art museum and the Miro Museum. The city has many other museums that are no problem whatsoever; the Picasso Museum is the only that was a problem for me; it was a total madhouse.

We were there last October. We had pre booked the Sagrada Familia only. We purchased the Mila tickets while there before closing for the next day, no line. But, we couldn’t get tickets to the Picasso Museum, they were fully booked.

Thank you, Barbara that's good to know about the Picasso Museum. I've been there twice and walked in without standing in line. Things change!
You also want to pre-book for the Sagrada Familia and if you visit Dali’s Theatre-Museum in Figueres you need advance tickets there too.

I have been to Barcelona twice in the past year. Everything already said by others is correct. There are so many tourists in Barcelona that buying advanced tickets makes sense for anything that is famous. Some sites that do not get as much attention, but are definitely worth the visit, though, are Casa Vicens, MNAC, and the Recinte Modernista de Sant Pau. You won't find the suffocating crowds in those places. You can buy tickets for Casa Vicens (a little out of the normal tourist area, so riding the metro is helpful) on their website that are good for any time, so you don't have to worry about when you want to go. Also, most of the museums are free on the first Sunday of the month, but you have to reserve a spot ahead of time online, since it is understandably popular. in addition, this is not about whether or not to buy ahead, but if you visit Park Guell, there are several other "back door" entrances that are not clogged at all. If you grab a sandwich at the nearby Guelly Sandwich Park, you can just walk up the hill and eat your meal at a picnic table, and then walk into the park without any fanfare or lines. There is a small booth for tickets, but that's it. Enjoy your visit!

Ditto.
Albeit we get tourism all year round, you're visiting in one of the worst months, so pre-book everything that's pre-bookable and put your mind to rest. In order to know what can be booked simply look up the official website, if purchasing a ticket is available, consider doing so.