A foam is just a liquid with plenty of air incorporated into it. You can incorporate air into any liquid; in order to be able to create an actual foam, however, you need to be able to incorporate the air faster than it escapes.
What makes a liquid able to hold the air you're incorporating (and hence form a foam) is a foam stabilizer, also commonly called an emulsifier1. I know of no specific taxonomy of stabilizers, but the vast majority are hydrocolloids AKA gelling agents and belong to some family of protein.
- Agar, carrageenan, alginate, xanthan, and pectin are all types of polysaccharide;
- Lecithin is mostly a random collection of phospholipids;
- Gelatin is denatured collagen, i.e. animal protein;
- Whey protein is the prevalent protein in dairy products;
And so on. Really almost any emulsifier will do. Basically everything in your list either is, or contains, one of the the additives mentioned above:
- Chocolate is almost always emulsified with soy lecithin;
- Eggs contain high amounts of lecithin;
- Milk and cream contain whey protein;
- Most "supermarket cream" also has emulsifiers like carrageenan already in it.
...you get the picture, I hope. The most basic answer I can give to this is that if you want to make a foam, you need to either use something that's already an emulsion (milk, butter, chocolate, etc.) or use an emulsifier/stabilizer additive (such as gelatin, lecithin, etc.)
If you want a relatively complete list of all of the food additives that qualify, you'll want to look at the E number, and specifically E400-499 (thickeners, stabilizers, emulsifiers).
1. As commenter Erik very correctly points out, an emulsifier is not the same thing as a foam stabilizer. However, by convention, the terms seem to be used interchangeably all over the place, to the extent that I get blank looks when I refer to a "stabilizer" as opposed to "emulsifier". So, know the difference, but don't get too hung up on it.
Best Answer
The cream whipper relies on gas expansion to work.
When you make whipped cream by beating, you beat fine air bubbles into the cream. The cream traps air and becomes essentially a matrix that holds those bubbles--a foam.
Your gas-charged whipper does the same thing in a totally different way.
When you charge the whipper with gas, there's high gas pressure inside with the cream. The cream will actually absorb the nitrous oxide you put in. Because of the pressure, the gas absorbed can be thought of as really really really small bubbles within the cream. So you have a matrix of gas and cream, but because the bubbles are so small, it's essentially just cream.
Chilled liquids more easily absorb gases at high pressure, which is why it's good to use cold cream and keep the whole unit in the fridge. A limited amount of agitation (shaking) exposes more cream to the gas, improving absorption.
When you release the cream from the device, the absorbed gas expands rapidly. The bubbles get bigger, and your cream to bubble ratio becomes more like the foam that we know as whipped cream. It's really exactly the same thing, only with nitrous oxide instead of plain ol' boring air inside the bubbles.
Why nitrous oxide? As I understand it, it's because it's the cheapest non-toxic, odorless and tasteless gas you can get. Carbon dioxide would almost be a good choice, but unfortunately it's bitter. Not a good match for cream.
Finally, why is shaking too much a bad thing? That one I don't know for sure, but I know what happens when you over-whip cream with the mixer. You make butter. Perhaps the gas or high pressure encourages this conversion, or maybe you're just churning it that much when you over-shake. Either way, I'm sure you've essentially made butter when you shook it too much.