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Can you rip materials that are not perforated on shabbat or yom tov? Can you rip out a piece of aluminum foil using the tool found on all foil boxes? Can you rip toilet paper not along the perforated line but in between the perforations? Can you rip a piece of paper in half?
What sort of considerations should you take into account before ripping non-perforated materials - granted that you are allowed to do so.
So you're asking a very broad question here. The short answer to your question is that there is a melacha of Tearing (קורע) besides for the issue of the perforations (מחתך).
First is the issue of Tearing, on which there are different opinions. To quote myself in another answer:
The Shulchan Aruch HaRav (340:17) (and I believe, the Minchas Chinuch) holds that the melacha of tearing only applies to composite items. I.e., fabrics, which are made from multiple threads, or anything else that is two or more items connected together. Therefore, there is no prohibition, Biblical or Rabbinic, against tearing paper or similar items.
On the other hand, the Mishna Berura (340:41) holds that tearing paper is a violation of the melacha of tearing.
But wait -- there's more! The things you mentioned -- toilet paper, aluminum foil -- present another problem, that of Tikkun Maneh. Essentially, by separating the toilet paper or foil, one is "creating" a new useful object, and this is forbidden as a sub-category of Makeh B'Patish. These tearings are constructive and therefore forbidden, even by those who would otherwise permit them.
Obviously, for practical halachah, one should consult ones local Halachic Authority, and not rely on anonymous interneters.
