Are there rules to poetry? Do all poems have to follow some kind of structure? Because the poems I write don't, they're just sentences that don't rhyme. Do you put something like that into a certain category?
I think it would be fairly hard to miss, in ready any modern poetry collection, that some poetry does not rhyme and there are no rules about how to write it?
I wouldn't say there are any rules exactly. But even poems that appear completely random are usually very cleverly thought out - word choice, placement of lines, development of ideas etc. Yes, what you write is free-verse.
Personally I find writing free verse an awful lot harder. Metre and rhyme provide a template, give you a pattern to follow. To write good free verse the writer has to have such a developed sense of language, such a feeling for sound, for cadence, for the explicit and implicit meanings of words in order to be able to construct a poem 'free-form' knowing, without the yardsticks of traditional poetic structure to measure it by, that what they have written has intrinsic quality.
Poetry as a form of personal expression is a perfectly valid exercise, so I wouldn't suggest everyone who wishes to write a poem must first master the basics of metre and rhyme. But if a person wishes to become a craftsman (woman) in the art of poetry, it's no bad thing to develop an adeptness in all of its crafts.