I haven't played a Draft tournament in years, but I always thought it'd be neato to retain one's draft deck post-tourney as a keepsake and as-is. Were I to have done so, I'd have several samey decks with which to fondly reminisce. Of course lands are interchangeable for such concerns...

I don't keep my draft decks, but the limited decks I make at prereleases often form the basis for the decks I use in constructed.

I've never kept a draft deck intact. For me, the drafting portion is the rewarding part, so actually having the deck afterward doesn't do me much good.

I just write them down. Or I used to, when I used to post them here.

When I'm done a draft night (or a prerelease), I tend to enter all of my newly acquired cards as a new deck in Decked Builder (the cards I actually played as the deck, all the cards I didn't play including winnings as sideboard). And usually I save it with a name identifying the block and night of draft, before I proceed to hit the 'add deck to collection' button (and then proceed to fix the foils, because it adds them by default as nonfoils). As a result I tend to have a virtual record of my drafted decks, and I could reconstitute them at will (if I haven't actually parted with the cards).

Though in retrospect (looking at my list of old saved decks now), I don't seem to be as particular about naming as I intended to be. I see "conspiracydrafted.dec", "conspiracydraftnite2.dec", "earlybfz.dec", "fnmkhans1.dec", "nov1414draft.dec", "oct24khansdraft.dec", "dtkPrerelease.dec", etc. All of them deficiently named in some way.

MtGO does that for me. Every now and then, I clean up the folder with freeform decks, as otherwise it's almost impossible to find the recent ones. I also usually take a screenshot and save it, named after the set and date drafted (yes I only draft once a day, and even then not every day). Sometimes I even post them here. ATM, BFZ is old news and I'm not drafting the cube, but I plan on posting a few when Origins will be new.