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It is not very odd in spiritual teachings to deny the existence of the future and the past, there is only 'now'.
But are there philosophers who also denied the existence of the future and past?
It seems to me that the more empirical theories would deny them too because the future can't be experienced. Does Hume deny them? Or other philosophers.
Or are the only ones who think it exists are some idealists like Plato?
Presentism is the view that only the present exists, see the SEP article on Time, Section 6. "Presentism, Eternalism, and The Growing Universe Theory", and the IEP article on time, Section 9.a . Presentists argue that we cannot speak of things existing in the past or in the future. For something to exist by definition means that it has to exist in the present. Statements about the past are only true insofar as they have effects on the present: For example we can say that it is true that dinosaurs existed in the past only because there is present state of affairs (fossils, evolutionary biology, etc...) that is traceable to the existence of dinosaurs. Similarly, the statement "I will die someday" is true by virtue of the present fact that I am a biological being, not by the truth value of the future event in itself.
Closely related to the topic is John Mctaggart's A/B Time theory (McTaggart, J.E., 'The Unreality of Time', Mind, 1908.), which states that time is unreal. It is not that only the present exits, but that the whole notion of time is an illusion, based on the idea that past, present, and future, exist only relative to each other, and not any fixed outside reference.
Hume doesn't deny the reality of the past and the future, but true to his empiricist principles, attributes them to our interpretation of sense data, not to any fixed outside passage of time. See the IEP article on Hume, Section 3.b.
As an addendum to Alexander's answer, what you find sometimes is that what is denied is the reality of the future. The idea, that can be linked to Dummett, is that, because statements about the future (e.g. tomorrow it will rain) do not have a fixed truth-value, we should be anti-realists about it. This should not be interpreted quite as saying that the future doesn't exist or that talk of the future is illegitimate though; one might, for instance, think that we ought to reason intuitionistically about the future.
Of course, fatalists deny that statements about the future don't have a fixed truth-value.
This question contains a linguistic trap. In English (as well as most languages I'm familiar with -- I've heard that there are Bantu languages where this is not true) "exists" means "exists in the present".
Therefore, "does x exist" means "does x exist in the present". The answer to the question "does the past (or the future) exist in the present" would seem to be no.
On the other hand, answers to "did the past exist in the past" and "will the future exist in the future" would seem to be yes and yes, almost by definition.
Thinking about time can be helped by using common sense terminology. I would say that the past, present and future consist of events, not objects. Concerning events, we should ask not whether they exist/existed/will exist, but if they happened/are happening/will happen.
Common sense would say that past events happened in the past, present events are happening now, and future events will happen in the future.
I think that many arguments against the existence of the past and the future are founded on intuitions prompted by misleading terminology.
Or are the only ones who think it [ past,future ] exists are some idealists like Plato?
More Aristotle than Plato. Aristotle stands out as the sort of objective reality, existence exists, things are what they are philosopher of antiquity. If alive today and consistently pro-reason, where he might brush himself up informationally--in the realm in cosmology and metaphysics. He'd likely hat tip the laws in physics where matter and energy are in continued transformation, and the universe. Everything that exists as a whole. Is eternal. Is out of time or forever. In that sense there definitely being a future. The past being just that; no matter the time measurement (say, a specific phase of the previous Earth orbit of the sun). Where time is simply a relative-measurement concept off the property of causation known as sequentiality.
