Philosophers have many differing views on what the fundamental categories of being are. In no particular order, here are at least some items that have been regarded as categories of being by someone or other:
[edit]Physical objects
Physical objects are beings; certainly they are said to be in the simple sense that they exist all around us. So a house is a being, a person's body is a being, a tree is a being, a cloud is a being, and so on. They are beings because, and in the sense that, they are physical objects. One might also call them bodies, or physical particulars, or concrete things, or matter, or maybe substances (but bear in mind the word 'substance' has some special philosophical meanings).
[edit]MindsClasses
We can talk about all human beings, and the planets, and all engines as belonging to classes. Within the class of human beings are all of the human beings, or the extension of the term 'human being'. In the class of planets would be Mercury, Venus, the Earth, and all the other planets that there might be in the universe. Classes, in addition to each of their members, are often taken to be beings. Surely we can say that in some sense, the class of planets is, or has being. Classes are usually taken to be abstract objects, like sets; 'class' is often regarded as equivalent, or nearly equivalent, in meaning to 'set'. Denying that classes and sets exist is the contemporary meaning of nominalism.
[edit]Properties
The redness of a red apple, or more to the point, the redness all red things share, is a property. One could also call it an attribute of the apple. Very roughly put, a property is just a quality that describes an object. This will not do as a definition of the word 'property' because, like 'attribute', 'quality' is a near-synonym of 'property'. But these synonyms can at least help us to get a fix on the concept we are talking about. Whenever one talks about the size, color, weight, composition, and so forth, of an object, one is talking about the properties of that object. Some-though this is a point of severe contention in the problem of universals -- believe that properties are beings; the redness of all apples is something that is. To deny that universals exist is the scholastic variant of nominalism.
[edit]Relations
An apple sitting on a table is in a relation to the table it sits on. So we can say that there is a relation between the apple and the table: namely, the relation of sitting-on. So, some say, we can say that that relation has being. For another example, the Washington Monument is taller than the White House. Being-taller-than is a relation between the two buildings. We can say that that relation has being as well. This, too, is a point of contention in the problem of universals.
[edit]Space and Time
Space and time are what physical objects are extended into. There is debate as to whether time exists only in the present or whether far away times are just as real as far away spaces, and there is debate as to whether space is curved. Many contemporary thinkers actually suggest that time is the fourth dimension, thus reducing space and time to one distinct ontological entity, the space-time continuum.
[edit]Propositions
Propositions are units of meaning. They should not be confused with declarative sentences, which are just sets of words in languages that refer to propositions. Declarative sentences, ontologically speaking, are thus ideas, a property of substances (minds), rather than a distinct ontological category. For instance, the English declarative sentence "snow is white" refers to the same proposition as the equivalent French declarative sentence "la neige est blanche"; two sentences, one proposition. Similarly, one declarative sentence can refer to many propositions; for instance, "I am hungry" changes meaning (i.e. refers to different propositions) depending on the person uttering it.
[edit]Events
Events are that which can be said to occur. To illustrate, consider the claim "John went to a ballgame"; if true, then we must ontologically account for every entity in the sentence. "John" refers to a substance. But what does "went to a ballgame" refer to? It seems wrong to say that "went to a ballgame" is a property that instantiates John, because "went to a ballgame" does not seem to be the same ontological kind of thing as, for instance, redness. Thus, events arguably deserve their own ontological category.
Properties, relations, and classes are supposed to be abstract, rather than concrete. Many philosophers say that properties and relations have an abstract existence, and that physical objects have a concrete existence. That, perhaps, is the paradigm case of a difference in ways in which items can be said to be, or to have being.
Many philosophers have attempted to reduce the number of distinct ontological categories. For instance, David Hume famously regarded Space and Time as nothing more than psychological facts about human beings, which would effectively reduce Space and Time to ideas, which are properties of humans (substances). Nominalists and realists argue over the existence of properties and relations. Finally, events and propositions have been argued to be reducible to sets (classes) of substances and other such categories.