I think alignment should be a separate "module" that provides no mechanical benefits or penalties whatsoever. No preventing lawfuls from being bards because the bardic wanderlust could never be felt by a lawful individual. No hamstringing good-aligned characters by making them more vulnerable to key attacks from evil monsters. And absolutely no level or XP losses from the "trauma" of changing alignment.
Once that point is out of the way, we can talk about how to make alignment an enjoyable addition to the game rather than the straitjacket it sometimes became in the past.
And on that point, I'd like to see D&D return to the iconic 9-position alignment system. It has entered popular culture; it harkens back to the Gygax/Moorcock roots of the AD&D alignment system; but most importantly, it helps even novice players understand that not all flavors of good are alike. Over the years, I've seen how that last point makes for a a richer experience around the gaming table, and it's something that I hope will be considered as the new edition takes shape.
But, I do think the 5e team needs to think more carefully about what "law" and "chaos" mean. 3e told us that lawful characters keep their word, judge those who fall short in their duties, respect authority, tend to lack creativity, refuse to use poison, and have a code of conduct. This definition combines ethical precepts (keeping one's word), personality quirks (judging others), and aptitudes (lacking creativity) with the notion that one is somehow bound by what others say (respecting authority). When one compares that to the relatively simple and streamlined definition of goodness as "willing to make sacrifices on behalf of others," the contrast is clear.
What I mean by that is, alignment works best when it serves as a shorthand for how characters will act regardless of the campaign setting into which they're placed. If I find out that a particular character is good-aligned, for example, I know immediately that she will generally try to help people, even if two different good-aligned people might disagree on exactly how to do that. But if I find out she's lawful, I need an allegiance-style breakdown of exactly which laws or authorities or codes of conduct she respects before I can say what her general inclinations will be, which defeats the main purpose of having an alignment system in the first place.
This is not to say an allegiance-type system is "bad" -- we've informally used it for years in the 4e campaign I run as well as the Pathfinder campaign in which I participate. But it isn't, and can't be, a substitute for a simple two-word phrase that gives you a setting-free idea of the values for which any given character stands. This might be based on social order versus individual freedom. It might be whether the ends justify the means. It might even be whether one desires modron-like stagnancy or abyssal instability (though I wouldn't personally prefer this). But it has to be something.
With those caveats in mind, I'm hoping for a new and improved 9-position alignment system for 5e.