Rubber: Like cork, rubber can be installed in tiles or rolls. Rolls can come in quite long lengths at 36-48" widths, making for few joints (thus fewer places for potential problems). Just imagine - a roll of rubber flooring could be laid with no joints at all in a galley kitchen! Rubber can also provide additional traction in the kitchen - especially with raised dot rubber floors as shown in image 3 above.
Linoleum: One more forgiving flooring material is good old traditional linoleum. Linoleum is a natural material, made of linseed oil, pine rosin, ground cork dust, and wood flour. It is a flexible material that dates back to the 1800's and, like cork and rubber, comes in tiles and rolls. It is often pigmented to allow for decorative patterning as seen in image 4 above.
A terrific, high-quality resource for cork and rubber floors is Expanko Inc. And if you're looking for linoleum, the go-to source is Marmorette by Armstrong.
Related: Rubber Floors In the Kitchen
(Images: Expanko Inc, Living Etc., kitchenideas.com.au, Country Living)