Alignment has had a storied history in D&D. It actually started back in Chainmail (the precursor to D&D) as a simple faction system - Good armies could ally with either Lawful or Chaotic ones (but not both at the same time), but not Evil armies. For that purpose it worked reasonably well, although if designing Chainmail now I would instead opt for five much more 'generic' faction names - White, Green, Black, Blue, and Red (or something), each of which had two potential allies and two sworn foes - the standard Rock, Paper, Scissors, Lizard, Spock configuration. (Actually, I'd probably include a secret sixth faction that was opposed to all the others...)
Anyway, ever since its origin as an almost pure team-shirt view of things, D&D alignment has accumulated a whole load of stuff... most of it awful.
Eventually, D&D 4e dropped all the residual mechanical implications of alignment, but failed to take the final step of disposing of it entirely. And 5e then repeated that mistake. (I find myself in the odd position that I was actually fine with alignment as it was, mechanical teeth and all; or I'm fine with it being removed entirely. But leave it as a withered appendix, and it infuriates me.)
I've now reached the stage where not only did I drop alignment from my character sheet redesign entirely, but before that I actively advised players to leave the box blank - that is, I advised against stating any alignment even for their own use. The big issue there being that those two words seem to exert an obscure power - put them on the character sheet and they seem to affect the way the player runs the character, even where they really should not. Better just to get rid.
And yet...
One of the quite nice features of 5e is that players are encouraged to give a bit more thought to role-playing than previously, with the character sheet including little boxes for Traits, Ideals, Bonds, and Flaws. In some of the later books they've introduced a few new flavours of these things. I find I like those, even if I have divorced them from the Inspiration mechanic. (And that, of course, means they become a matter of "you can pay as much, or as little, attention to these as you want".)
And yet, and yet... I have found in my recent campaign that some players painstakingly fill in every box on the character sheet, some completely ignored Traits et al, and some filled in some of them. This left valuable character sheet real-estate unused and wasted. And, of course, if you're using some of the alternatives, there was then no box at all.
The way I've dealt with that in my redesign is to place a "role-playing notes" box on the second sheet, freeing up much-needed space on the front for more class features. That largish box then allows the player to define as much, or as little, about the character as they wish.
And now, to the point. For various reasons, I've found myself working with a whole load of pre-gen characters recently, and one of the things that I've suddenly found quite useful is to add an alignment to the box - crucially including a few words on what that alignment means to that character. That means that two Lawful Good characters could have significantly different statements of their alignment, but that's a feature rather than a bug. (And, actually, there's nothing to stop a player declaring an alignment and then immediately subverting it, giving a character who thinks of himself as Good but who is anything but.)
Which I actually find I like a lot more than I thought I did.
The other thing I use that box on the character sheet for is some sort of a tie to the campaign's "side dish". For instance, in "The Mists of Lamordia" the box contains a note about the character's personal secret. For the pre-gens for "Lost Mine of Phandelver", each of the pre-gens has a Personal Goal. And for "The Quest for Memory", each of the characters would have been assigned a Quest. Technically, this also falls into the category of "use this or ignore it as much as you want." In practice, though, since the "side dish" ties into the way I award XP these days, it is unlikely to go completely ignored.