Well I don't read FF comics. What aspects are non-negotiable when making a movie? Does it have to be over-the-top goofy? Do the Four have to be celebrities? Does Reed have to be an inventor? Does Doom have to be the center of all villainous plots?
I would say that you have to respect Ben Grimm / The Thing. Ben is Jack Kirby (co-creator of the Fantastic Four) - the cigar chomping, gruff, bruiser with a heart of gold who's smarter and more talented than he appears to be. Ben is the heart of the FF and a piece of the man who brought it all to life.
From what I hear, the new movie kind of marginalized Ben; but the little development he was given was to show him as someone who had an abusive childhood. That works for Hulk; but it's not Ben. Some unused footage seems to indicate that Trank got it right at one point; it showed Ben as a baseball player and allegedly before each game his coach would give the battle cry "It's Clobberin' Time!" That could fit Ben.
Torch is the comic foil to the group and that should be there. Chris Evans and Michael Chiklis really nailed the two characters in my opinion. Reed and Sue are kind of blank archetypes really; Reed is the living exposition to what's going on, and writers have been trying to figure out what to do with Sue for a long time. There's room to grow there, but the main aspect of the Reed character is his intelligence and inventions; without that, you have a different character. It would be like saying we're going to take MacGyver in a new direction where he doesn't make stuff.
I do think their celebrity status is important; and even the comics have addressed how the world reacts to the reality bending experiments taking place in the Baxter Building in New York (currently the FF has been evicted and the building was brought by Peter Parker as the new HQ of his multi-million dollar company Parker Industries).
As for Doom, he didn't appear in the comics until issue 5, and I don't see him as the center of the FF world. Doom would be off doing his own thing and not even noticing the Fantastic Four except that Reed Richards is part of it. Doom and Reed went to college together, and Doom blames Reed for the lab explosion that disfigured his face (leading Doom to wear the iron mask). The reality is that the explosion occurred because Doom was hasty; Reed tried to warn him the machine was going to blow up, but Doom wouldn't listen to him. Doom started there using Reed as the scape goat for all his failures and it's just never ended; if something doesn't go Doom's way, it must be because of something Richards did.
The interesting thing in the comics is that the lab explosion actually only left a tiny scar on Doom's cheek; but Doom was so vain and OCD about his appearance that he freaked out. Doom went to live with monks for awhile where they forged the mask for him to try to help him overcome his obsession about his face; but Doom was impatient and put the mask on while it was still heated from the forging. That is what led to his face being horribly disfigured; it wasn't Reed at all.
However, the thing with Doom is that he's pretty much the FF's Lex Luthor. Doom obsessively hates Reed, so he's always going to be pushing himself into the FF world just for that reason.
As for other villains in the FF universe, the biggest one is probably the Skrulls (and that's likely the key reason why Marvel Studios wants the FF license back). The Skrulls are shape changing aliens that have been a big part of Avengers stories (including a big one called Secret Invasion); but they first appeared in Fantastic Four, so they are part of that license. Marvel Studios also needs the FF license back to use the big Avengers villain Kang the Conqueror (who first appeared in Fantastic Four as Rama Tut).
The remaining rogues gallery of people like Puppet Master, Mole Man and the Frightful Four are better served in something like television; the only truly epic things left are Annihilus (the insect emperor of the Negative Zone dimension), Galactus and his heralds and Namor the Submariner (whose movie rights are tied up at Universal Studios).