First of all you would rule out bones or the like, because they would impede stretching or compressing beyond a small amount. You see something like that in an octopus, who can pass through narrow passages just by squeezing its body through them, thanks to the lack of bones.
To have a rubber like behavior also the body would be made in a rubber like way: long and loosely bound molecular chains which, in the unstrained state are randomly garbled up and which with an imposed deformation tend to align in a single direction, allowing for elastic deformation.
However you would still be bound to the conservation of volume: a volume delimited by a surface of 10 square units and with a length of 10 units would stretch to 100 units of length with a cross section of 1 square units, but it would reach a point where it cannot stretch further (which is not a feature for Mr. Fantastic, AFAIK).
Overall I doubt that a creature with this feature would be much more different than a blob or a goo, because of the very way it is made. Nothing like a humanoid in the examples you gave.