Freezing is bad for things which have a special structure and lots of water. Everything else should be OK with freezing.
The prime example of a thing which behaves badly when frozen is a fruit. It consists mostly of water, but is firm instead of liquid because the water is contained within a cellulose structure created by the cell walls of the fruit. When you freeze it, the water turns to sharp ice crystals, which also expand in volume (water is one of the few liquids which does that upon freezing), and they hurt the cell walls. When you defrost the fruit, it turns terribly soft, and all the juice runs out. It is practically like maceration without the sugar. You can use the fruit for cooking, e.g. for a jelly, but it is not the same thing as a fresh fruit.
Another example which is very structure dependent is whipped egg white. It is a fragile foam, and the formation of ice crystals is also very damaging for it. Whipped cream is similar - you can freeze it (and get ice cream), but it melts to a liquid, not a foam.
On the other hand, foods which have a specific structure but not much water are OK with freezing. Butter is not pure fat, it is an emulsion of 17% water in 83% fat. Emulsions tend to have very fragile structures (don't freeze mayonnaise), but butter is OK, because there isn't much water so the formation of crystals doesn't disrupt the structure. Another exception which is OK to freeze is dough. A dough being practically a mesh of gluten, it doesn't get really hurt by the crystals.
There are a few ingredients which develop an off taste when frozen. For example, don't freeze anything carbonated, it tastes terrible afterwards.
You should also consider the problem of freezer burn. It happens when the moisture of the frozen product sublimates in the dry freezer air. To prevent it, you have to seal the food airtight. You are therefore limited by the kind of food you can seal. If you have a food which would make a mess in a home vacuum sealer, like a wet stew, you could try freezing it for a night, so it is hard but does not have freezer burn yet, and then sealing the frozen chunk and returning it to the freezer.
Some ingredients will prevent the food from freezing into a solid block. Notable examples are salt, alcohol and propylene glycol (which is used as a solvent in food coloring and baking aromas). This shouldn't be a food safety problem, because first, bacteria growth is inhibited by low temperatures, and second, if you have these things in concentration high enough to completely prevent freezing at -18°C, then they will kill the bacteria by themselves. But it can cause some logistic problems if the food stays too soft.
As you see, these general guidelines have exceptions, or at least require some knowledge of what food is built like (but frankly, I would have predicted that yeast dough freezes badly if I didn't know from experience that it works well). So you should definitely try to remember it on a per-case basis for the most common things you intend to freeze. A very convenient guideline is to think if you can buy a premade equivalent frozen at the supermarket. If they sell it, it will probably turn out OK when frozen at home (sometimes with differences, like frozen fruit). If they don't have the food (or its major ingredients), there is probably a reason for that.