I think you can break it down into a few categories but there are exceptions for each:
- Should be indistinguishable from the comics. Best example is Spidey's webshooters. But the counterexample is Thor stamping his hammer on the ground to make thunderstorms.
- Can be altered to modernize, but should hold solid ties to the comics. Bruce Waynes parents need
to be murdered, but Tony Stark can be held hostage by terrorists rather than communists.
- The origin and powers of the villains should follow the above criteria. No robotic Green Goblin suit
, but its okay that Two Face was burned instead of melted with acid (more realistic/modern?).
- Almost doesn't matter in most cases. Rachel Dawes: 100% Nolan's invention and perfectly functional. But Peter Parker changes from Gwen's death and almost requires both her and MJ for his story to be told properly.
- Besides key points (origin), chronological order need not be adapted. Certain things should just be dropped all together if they aren't used. Iron Monger can be Stark's first villain, but Spider-Man has to meet Gwen before he meets MJ.
In the end, as stated above, its case by case. As long as there is Potential for exploring the source material and Continuity within its own developed universe (I'm looking at you X-Men), I say pretty much anything goes.