I keep them, they're a crucial part of my timeline to where I am now even if they're super cringey. All the old ones I still have sit in a folder with plastic sleeves.
Post on Deviantart, it has "scraps" folder which is separated from your main gallery, a good way to store (and maybe earn views) from your sketch drawings
I have the majority of my drawings from childhood still, they sit in a few plastic drawers near my work station. I personally love looking back through all of my old stuff, especially from pre-middle school which was when I started "seriously" getting into drawing as a hobby, just to remember all the crazy stuff I did xD
Similarly to @Humbug there are a few notable missing things that I wish I could find but seem to either be gone or buried in storage somewhere though- One was a series of comics I made in elementary school about a rabbit named FRED- Funny Rabbit Except Dumb. Was just a grade-school level comedy strip that I'd like to re-live.
The other is a nartuo fan comic I made in middle school, just because A.) I can't remember if it was better or worse than the digimon one from the same era that I still have in my drawers and B.) I remember it being kind of mean because the main plot of the first chapter was a kid I didn't like in school getting assassinated and all of the self-insert MCs having to solve the mystery of whodunnit. While mean, also hilarious and similarly would like to see again xD
I keep my old DeviantArt accounts to keep an archive of my old work, but a lot of my really, really old work (like, middle school and early high school) I've thrown away in the name of trying to keep as few things as possible in preparation for a big move.
It's nice to be able to see how far I've come, but a lot of it was just... the kind of elementary school stuff that your mom would put on the fridge to encourage you. And only a mom because her precious child made it. XD
On the other hand, I have a bunch of storage boxes for more recent art that I couldn't bear to get rid of yet because I'm still proud of it, or still remember being proud of it.
that's sad
I know stuff can get dusty
It was in a plastic container under my bed too! It shouldn't have gotten moldy! My room doesn't get moist and cold. If I store papers for long-term next time I'm going to be tossing those packets you get in jacket pockets and such - moisture suckers. You can get them by the bulk off ebay/amazon/ect I hear. That should help a lot.
Also don't store your papers and arts (paints and markers don't count really) in cardboard. That thing basically has mold written all over it. Especially corrugated cardboard.
It was and it wasn't? It was right after I finished Uni so it was like...letting go of the old me. That and I had to do it or I was trapped in my student apartment forever. 
I take a picture of it,and put the traditional art into an obscure place to be forgotten about.
it be nice to remember the cringe,later in the future
Well i made a weird doodle years ago (probably even before i made comics) and i introduced that as a one time character (an alien barman).
I keep everything, actually. I doodled a lot of weird character designs, and have concept art of more than a dozen scrapped stories. I keep these designs around so's that, whenever I need to make a new character or concept for something I'm currently writing, I look through those first and see if I can adapt a character from those instead.
That, and I can look through those and either A.) Find a design I like but forgot about or B.) See how much I've improved.
I keep my oldest artwork around, because whenever I look at my current art and feel that is not satisfying, I always look back at my old work to realize how far I've gone and continue to develop my art even better.
So they stay where they are.
I keep a lot of my stuff. I save the pieces I knew were my favorites or things I was proud of at the time I drew them. I think it's good to have a catalogue of your artistic journey so you have stuff to look back on 
I keep whatever I manage to save.
Ngl, almost all of my sketchbooks from previous years were all either thrown away or hidden away in some obscure part of my house. I'm very bad at keeping track of my own sketchbooks, which is a shame.
I still have [most] of my old digital drawings. I used to have a bunch of art drawin in dA Muro back when I actually used my dA, but I deleted them when I was about 13 because I was incredibly conscious of them. It was the age where "DeviantArt Cringe" videos and compilations were at the peak of its popularity, and I was afraid that I was gonna end up in one in some way or another and I'd be mocked forever o.o
Goes to prove cringe culture or whatever you call it is incredibly toxic to young artists lmao
Sacrifice it to the gods 
Or burn it. (Although these are not mutually exclusive...)
I do keep most of my old (traditional) art, but my archives go over a decade back, to way earlier than the start of my "woke" artist phase, and so a lot of it is... really really bad. This year I took some of those super-old arts and burned a lot. I scanned most of them, so at least I have something to cringe over that doesn't take up physical space... I also kept the ones I felt sentimental about, or were in some way important (eg. first image of a particular character).
@azzy-m Yeaaah cringe culture... I remember a very old tumblr blog called "Socially unacceptable art", created solely for mocking (supposedly) cringy art. A lot of it was very weird porn/fetish stuff, but some pieces were clearly drawn by beginner artists, maybe even children - I can only imagine how crushing it would be to find your drawing on a blog where it's made fun of by people older than you, when you're just a kid who likes drawing for fun 
I like cringing at my old art, though. No one can stop me from cringing at something I made myself. 
But at the same time I realize it's counter-productive...