I worry about people's expectations here.
When it comes to player characters, you're almost always better off by this three step guide:
1) Write down a textual description of your character and what he's or she's known to be capable of.
Use plain English, use no game term or numbers whatsoever (except possibly class and level). Only include actions you have actually used in play; the capabilities the character actually displays on a semi-regular basis.
2) Throw away or hide your old character sheet. Only look at your notes.
3) Create a completely new character using the new rules, where you use your notes to guide you.
This guide is given to you completely free. It is guaranteed to work between ANY TWO systems in the whole hobby, no exceptions.
OK, that's fine for characters - to a point. But monster stats? Adventure guidelines? Playstyle pointers? 1e and 3e and 4e all play quite differently from each other even beyond the mechanics.
The best a conversion guide can do is be a matchmaker. For 1E thru 3E the focus needs to be on things like "the 1E owlbear is much stronger than the 5E one, use monster x instead" (made up example), or "The 3E Wand of Powers has been considerably weakened in 5E, use staff Y instead".
Or, and this is what I'd prefer, something like "The 1e Owlbear is much stronger than the 5e one, to best emulate the 1e version make these changes to the Owlbear in the 5e Monster Manual". This is relevant for some monsters that have been drastically changed over the editions - compare, say, a 1e Ghost and a 5e Ghost.
And even then: what will they do about 3E's magic item economy. To me, that's the largest piece missing if I want to run a 3E game with 5th edition. Nothing suggests they will patch this.
Perhaps, but keep in mind magic item placement has always been the DM's purview in any edition (even if the printed rules tried to tell you different), so to get a 3e feel just ramp up the dungeon treasures a bit; and allow buying and selling of magic items. I'm not sure how well 3e's magic item creation rules would port into 5e, though.
For 4E, it's a whole new ball game entirely. If you want to run games with a 4E vibe, you want whole new rules subsystems. You can't really convert between 1/2/3/5E and 4E. You would need pages after pages of DMG inclusion-worthy rules systems to make the game work in the ways 4E adventures assume.
Perhaps, perhaps not. I know the conversion works the other way, as I've converted some 4e adventures for use in 1e without much problem; so it can be done.
And I would be very much surprised if WotC gave us anything even close to something that would transform 5E into a game with 4E:ish sensibilities.
You know, as much as I dislike 4e and would be happy to see it go away I find myself disagreeing here. I think WotC sees there's still quite a few people playing 4e and would like to do what they can to bring them into the 5e fold, so I'd be surprised if they didn't give a 4e-5e conversion a good try. Whether it'll be worth using, however, is anyone's guess.
Have low expectations on these conversion guides. Very low expectations.
Anything's better than nothing, I say; and even if what they do isn't perfect it'll at least be a jumping-off point for us to carry on from.
Lan-"and if they backwards-convert 5e material into 1e I'll be ecstatic"-efan
