BOTW is one of my favourite games of all time and I loved its showing at E3 2016, but I'd still call that year a bad show overall as, in my opinion, having just one solitary game to show is a travesty regardless of how good that game is.

It's pretty debatable. As many have said, 2010, 2014, 2017, and 2019 are pretty close contenders.
2010 had Skyward Sword, Kirby's Epic Yarn, DKC Returns, Goldeneye 007 remake, Epic Mickey, Golden Sun: Dark Dawn, the unveiling of the 3DS, and the return of Kid Icarus
2014 had the epic Iwata vs. Reggie fight, the Robot Chicken skits, Zelda BotW's first tease, Splatoon, Smash 4's E3 coverage and invitational, Yoshi's Wooly World, Captain Toad Treasure Tracker, Kirby and the Rainbow Curse, Hyrule Warriors, and the tease of Super Mario Maker (I didn't mention ones like Bayo 2 and Xenoblade X due to them already announced from previous events)
2017 had the tease of Metroid Prime 4 (which may have lost some points due to the restarting of development), the tease of Pokemon Sw/Sh (debatable on how people are reacting to it now due to the recent events), Kirby Star Allies, Rocket League, BotW's first DLC pack, Yoshi's Crafted World, and the blowout of Super Mario Odyssey
2019 had the two Smash Bros. Ultimate DLC reveals, Luigi's Mansion 3's blowout, Trials of Mana Remake, No More Heroes 3, The Witcher 3: Complete Edition, Animal Crossing New Horizons, and Zelda BotW 2, among others

I probably have some recency bias, but I think 2019 was the best one out of the 4. A lot of games announced or showcase of new features/footage and some neat surprises like The Witcher 3 having all the DLC along with the game in one cartridge with no need for online updates just to install it, Banjo-Kazooie finally making their MCU Spider-Man-like return to Nintendo through Smash Bros. Ultimate, Trials of Mana getting a remake along with the Collection of Mana finally coming West during that day, Panzaar Dragoon remake, No More Heroes 3, and Zelda BotW 2.

I will give props to 2016 and 2018. I know some are not fond of the one-game focuses, but Zelda BotW set the tone for a new journey for Nintendo and the blowout at E3 2016 stole the spotlight even from Sony. I remember there was a video of people running inside the convention and apparently it was just to play BotW. The Nintendo feel with Nintendo's booth being basically the Great Plateau also added some unique charm that I think very few game companies can match in regards to standing out in a convention. 2018 was probably uneven, but Super Smash Bros. Ultimate, in the end, warranted the big spotlight. At 14.73 million units (as of June 30, 2019) and counting, Smash Bros. Ultimate is a huge system seller and was advertised as the ultimate celebration of Nintendo and video games with every fighter from the past Smash games coming back along with new fighters taking the stage as well.

1. 2016 - Everything was Breath of the Wild, my favorite game ever. And we only saw the plateau. At that point, I expected a deserted world, similar to Metroid, without towns and every story bit will be hidden in old diaries and environments.
2. 2010 - Excellent pacing, outside of the Skyward Sword segment and the interference to the Wiimote. Highlights: Skyward Sword, Other M and 3DS reveal.
3. 2019 - Game after game. Amazing and perfect pace for a Direct. I was expecting a Banjo game announcement after the reveal in Smash. Highlights: Witcher 3 and Breath of the Wild 2.
4. 2017 - All day looking for the reactions of the Odyssey trailer and Metroid announcements. Highlights: Prime 4 announcement and Samus Returns.5. 2014 - Good games and the announcement for the brand new Zelda HD. Highlights: Zelda HD, Mario Maker (iirc it was announced in this year) and Splatoon.
6. 2013 - First E3 direct. It was very good. Highlights: Mario Kart 8 announcement, 3D World dissapointment (even when now I love the game), and the DK debacle announcement.
7. 2011 - Epic Zelda orchestra, but wtf, the amazing Skyward Sword and Ocarina of Time 3D's trailer didn't happen during the conference. Cool 3D show for the flagship 3DS, though and announcement for a new Luigi's Mansion. Highlights: Wii U trailer (I liked) and epic Zelda orchestra.
8. 2015 - Already dissapointed that Zelda was delayed and not going to be on the show, but still expecting something worth. Highlights: I ended loving Triforce Heroes and looking at the reactions for Amiibo festival. Lol.
9. 2012 - Didn't like it. Highlights: Cannot remember anything outside of the Nintendo Land's fireworks.

Edit: forgot about 2018. I'll put in 5th place, below 2017 and above 2013. Smash segment was boring to me. Highlights: Fortnite and Hollow Knight's shadowdrops.

E3 2013 is quite the anamoly; it is the only year not to receive a single vote for either "best" or "worst" so far.

In retrospective I think this E3 was actually quite good. It was the first E3 Direct and they showed Mario 3D World, Mario Kart 8, Tropical Freeze, Bayonetta 2, Smash and Xenoblade Chronicles X. Games that were way better than expected. But the damage was already done with the 2012 reveal of Wii U. Only a few people expected that the titles would be as good as they actually should be.

So maybe many peope were unsure in which direction Nintendo would go and they were not convinced what quality Nintendo games should have. And it was the first E3 without a live presentation and a Direct instead. Nintendo was confused what they should do – and consumers also. It's a E3 of uncertainty, attention and skepticism. Announcements of games for core gamers for a casual praised console. Everything was not coherent.

Well it was fine is the thing.  It was Nintendo's first non-live event so the presentation was still a bit dry, but they had a good number of trailers for quality stuff.  They had quality announcements but not as many as the other favourited years.  I look at it as being very solid, just not awesome.

There's was good content and surprises, it was the format that make it forgettable.

Nintendo fixed that problem in 2014.