Generally I don't care for remakes because so often it's either the studios looking to cash in on nostalgia or a name (Ghostbusters), a story simply no longer being relevant for audiences, or writers and/or directors not understanding what made the original work (Total Recall). Yes there are some movies I consider sacred (2001 and The Godfather immediately come to mind)
That said, I do think there are some titles that could be remade, either to improve or to update for today's audiences. Off the top of my head:
1. The Last Starfighter. With a solid script, a charismatic lead, and updated effects this could be a fantastic movie.
2. He-Man and the Masters of the Universe -- I think there's supposed to be one in the works, but this has gone in and out of development hell for years, so would be surprised if a studio will actually spend the $100M+ to get it made given the lackluster performance of properties like Power Rangers and TMNT2, and the diminishing returns on Transformers. The challenge is cracking the right look and feel, not to mention casting. While I don't believe I've ever watched the movie in its entirely because it was abysmal, I do think Dolph Lundgren had the right build. Then you've also got all these wacky 'roided out supporting characters and costumes. The movie would really have to thread the needle to be a success. But if they were to crack it, there would probably be an onslaught of cartoon movies like Thundercats, SilverHawks, etc.
3. Classic Battlestar Galactica -- The reboot was okay, but a movie based on the classic series would be a blast. The reboot was weighted down with grittier realism and heavier themes, whereas the classic could basically be a lighter space romp. A charismatic crew with attractive leads, updated classic uniforms, redesigned cylons, sleeker ships and updated effects would rock. Sure, it's a $100M+ risk, but it could relaunch the franchise.
4. Logan's Run -- This is another one that has been in and out of development hell, but could work well.
5. Excalibur -- In certain respect this movie is on my "sacred" list, but it is reboot worthy. There have been several attempts at the Arthurian legend, most recently Guy Ritchie's latest bomb. None have done it better than Excalibur. The movie would need some tweaks and could borrow some from Game of Thrones.
6. Fantastic Voyage -- I think this one is supposed to be getting remade by Guillermo del Toro next year, but I wouldn't be surprised to see it slip back in development hell. I've wanted to see a scientifically accurate update of this movie for years. The original was made in 1966. The tech could be modernized and modern effects and CGI environments to replace the sets.
XMEN franchise starting with Apocalypse
You said it. But wouldn't start with Apocalypse. There is no reason this franchise shouldn't be pulling in Avengers money except for the fact that Fox is completely bungling it by sticking with Singer and Kinberg. Whether or not the franchise goes back to Marvel or they work out a share deal, they should turn it over to a visionary director like James Gunn, recast, and make it a trilogy culminating with Apocalypse (which will give the audience time to wash away the bad taste from the last movie).
Ditto on Fantastic Four. Should easily be a $800M-$1.1B per outing. Another trilogy. Start with Mole Man and giant monsters in the first flick... introduce Doom in movie 2 ending with Doom triumphant... Conclude the Doom arc in movie 3. At the very end of movie #3 maybe a month after the team defeats Doom and celebrations have died down, you have Sue coming into Reed's Kirby-inspired lab, planning to tell him that she's pregnant. However the only thing she finds is a weird looking pulsating machine and there is a rift in the fabric of space. Reed is nowhere to be found, but on the computer screen are the words "Negative Zone", which opens up another movie or arc should the franchise be strong enough to continue.
Don't try to tackle Silver Surfer and Galactus. They are better in the Guardians of the Galaxy cosmic universe, so work out a share deal and maybe have the FF cameo in that adventure.