My cats like to chew on plants, but they don't ever seem to eat them. Well, usually--they really like eating grass though, and often prefer it over houseplants and peppers. Growing some "cat grass" (oats) in front of a window for the cats to eat fresh whenever they want (and encouraging/reminding them to do so) might keep them away from your other plants at least somewhat... but if the plants to be kept away from them are in their reach, they'll probably eventually get the urge to take a few bites/chews, so you probably can't completely rely on this.
Some cats are different than others though... some might not even care about plants too much, especially as they grow older. If yelled at, some of the more well-behaved cats might listen and learn not to bother the plants. I have two cats, brothers--and one I can trust around plants for the most part, but the other one I can't trust at all. One of them is also much more well behaved, with the other always seemingly trying to find things to do that he shouldn't be doing to amuse himself, and repeated yelling does nothing more than make him stop until the next time you aren't looking (ie., in a few minutes).
I've never had a problem with my cats pissing in plants like Avon mentioned though... but outside is a different story, all outdoor animals seem to love finding plants to piss on, and cats are especially fond of dry to semi-moist soil (ie. the garden) to bury their shit in. We never did have any big pots that are big enough for a cat to jump into, so that's probably it. As long as a cat is fixed at an early enough age, the only form of "territorial marking" it will likely do is rubbing you or other objects with its face. My cousin has one cat that just likes to jump up in a big pot that's sitting on the floor in the living room and lay down in the dirt beside the plant, but she doesn't piss in it. For some reason, she just feels comfortable laying down in it.
As for dogs--well, I don't know, because I can't stand dogs... but I do know they'll destroy a hell of a lot tougher objects than plants. My aunt and uncle's dogs destroyed my cousin's PS2 controller.
Conclusion: Yes, you should definitely watch your cats closely and put your plants where they're not easy to access. It's only a matter of time before a cat's curiosity and instincts kick in, and it doesn't take much to seriously damage a plant. Precaution and prevention is better than being too trustworthy.
That cat also went ham on some of my seedlings much earlier in the year. Knocked one off the shelf which shriveled up and died, knocked another one out of its pot that I was able to save, and chewed up a bunch of leaves on the others, but they lived. I no longer have that cat, fortunately the current cat isn't into terrorizing plants.
