Best day ever is really hard to choose, considering what you want depends on what mood you're in and blah blah blah...
That being said, my three days at Download 2013 were some of the best of my life. Just me, a buddy, awesome music, and alcohol for a whole weekend of sweet sweet independence. It was the first time I'd been away from home with friends, so.
Interrailing was amazing, too, for much the same reasons - and I was with some of my best friends this time, so even though we bickered like old married couples it led to memories we still joke about now.
The times I've been to the Hogmanay (New Year's) Festival on Princes Street in Edinburgh with my family have been amazing too. It's just a huge street party - the entirety of one of the largest streets in the city is completely full, rail to rail, of people getting drunk, singing Auld Lang Syne, dancing, and there are some amazing fireworks over the castle... :3 good times.
And going through Las Vegas, Death Valley, and Yosemite was one of the best weeks of my life. My god. I was only 10 and I still loved Vegas; it's spectacular and grandiose beyond belief. And the Grand Canyon, Death Valley, and Yosemite were natural wonders so magnificently beyond anything I'd seen before...
I could go on and on, but to be honest my favourite days can be characterised by the sharing of incredible, often novel experiences with family and friends. 8 love quiet days in as well, but they don't stick in my memory as much; I don't need them to, because the purpose of them is to relax and feel warm and snuggly and just enjoy that day for what it is: chill as fuck. Don't need to store that away in my mind.