Supernatural beings and the 31 planes of existence

Did the Buddha have any personal experience with maras and devas and supernatural beings in general?

1. We have no idea what the Buddha experienced - we know nothing at all about the Buddha as a person (not even his name). But the traditional stories about someone called "Buddha" certainly portray him as having such experiences. In this Buddhists myths and legends are much like any religious literature. If we take the Buddhists texts literally, then there is no reason not to also take religious texts like the Christian Bible literally also. Though the two are mutually exclusive on many matters.

2. Humans beings evolved to attribute agency to unexplained events, in fact most mammals and birds do this to some extent. And to attribute human qualities to such agents. This is why gods have human motivations. We also have a tolerance for minimally counter-intuitive concepts like invisible agents. Certain events like out-of-body experiences act to convince us of the required ontological dualism, so that belief in a disembodied mind is possible. Without a careful analysis such things seem plausible to most people. But with careful analysis invisible agents vanish (as it were). See also Why Are Karma and Rebirth (Still) Plausible (for Many People)? Part I and Part II which summarise ideas from Justin L Barrett's book on the psychology of belief and relate them to Buddhist beliefs.

3. Early Buddhists adopted supernatural beings from local animistic cults (rukkhadevatā, yakkha, nāga, kinnnara etc) as well as gods from Brahmanism (Brahmā, Indra aka Sakka, and Agni; and more generally the devas and asuras). They also adapted some other beliefs from Brahmanism, often in the form of some kind of parody, such as hungry ghosts (preta - literally "the departed"), the spirits of the recently dead, to which Brahmins made food offerings to sustain them on their journey to Brahman. The idea of Hell probably came from Zoroastrianism. There do not seem to be any characteristically "Buddhist" supernatural agents, except for the Buddha himself who is apparently able to see back in time, travel to heavenly worlds, see the spirits of the departed, fly through the air, and read minds. Such skills as we rarely see these days.

4. Unfortunately for Buddhism, the laws of physics now completely preclude life after death. See my essay There is No Life After Death, Sorry. Unfortunately there is just no way to accommodate invisible agents that can interact with matter and remain undetectable by scientific instruments. Either something interacts with matter in a way that makes a difference on the human scale, and we can see how this happens because it happens on a human scale, in which case we ought to be able to incorporate it into theories of matter; or no such interactions take place, and we must seek other explanations for the things we believe to be supernatural agents.

Taken together we see that this kind of question makes many assumptions that are not valid. Once we eliminate the parts of it that are based on one or another fallacy, there is nothing left to answer. The best we can do is rephrase it in terms of what the tradition says about the mythical Buddha.

Is the mythical Buddha portrayed as having experiences of supernatural beings? Yes, he is. He is portrayed, for example, as able to travel to the deva and Brahmā worlds at will. And he can see where beings are born after they die. He also converses with yakkhas and devas, often devas that no one else can see. In the tradition the Buddha himself has all kinds of supernatural abilities. Indeed over time the Buddha came to be attribute with more and greater supernatural abilities and magical abilities, and ultimately Gautama became a mere physical manifestation of a cosmic principle of Buddhahood (which is an idea that parallels the Upaniṣadic brahman).

It is very clear to me that Maras, Devas and other supernatural beings are real phenomena that you can observe directly, if you know where to look. When ancients spoke of souls, spirits, demons etc. they were not crazy. They just did not mean it in the naive sense we think they meant it.

First, it might help to probe the meaning of "supernatural" in the Buddhist context. I think this blog post covers it pretty well. In particular:

The very notion of ‘Supernatural’ is one that, it seems to me, arises from Western philosophical assumptions. the basic idea is that there is ‘this world’, which is rational and subject to explanation according to the laws of physics, and the ‘other world’, which operates according to a quite different set of principles, and where the laws of physics no longer apply.

In Buddhism, however, the essential description of the world is not provided by the laws of physics, or other material phenomena. The most important ‘laws’ are the three characteristics – impermanence, suffering, not-self. And these describe any other state of being just as well as they describe ours. For theistic religions, ‘heaven’ is eternal – that is, not subject to conditions, and independent from Time. But for Buddhists, heaven is just as temporary as anything else.

The Sri Lankan philosopher David Kalupahana has developed this idea in detail. he argues that Buddhism is empirical through and through; that even those aspects of Buddhist belief that seem to invoke the ‘supernatural’ in fact merely involve a refining and extension of ordinary sensory capacities.

Starting from that perspective, I would say: yes, in every tradition of Buddhism I'm aware of it is agreed that Buddha knew the beings we refer to as "supernatural" in our culture - which, from a Buddhist perspective, are just other varieties of sentient beings. Because Buddha is omniscient, he has the same comprehensive knowledge of these beings as of any other sentient being. As summarized here, that knowledge includes:

(3) The force of being omnisciently aware of the various spiritual aspirations (mos-pa) of all limited beings (sentient beings): the inferior ones for this life, the middling ones for liberation, the superior ones for enlightenment, and those that are concealed (unconscious or expressed unclearly). In this way, he can guide each being accordingly.

(4) The force of being omnisciently aware of the source of everyone’s cognitions, as well as the source of their enlightenment (khams, their Buddha family-traits, Buddha-natures). He knows where all their thoughts, ideas, and misunderstandings have come from and also those factors in each of them that will lead to their realization of their fullest potential. In this way, he can correct all others when they have gone astray and draw out their strongest points.

(5) The force of being omnisciently aware of the superior and less-than-superior levels of everyone’s powers (dbang-po). Thus, he always teaches others in accordance with their intelligence and abilities so that they never become discouraged.

Sorry, but I am not familiar with the "31 planes of existence" so hopefully someone else can speak to that specifically. But the bottom line to me is that if Buddha knows all beings, he knows their various abodes as well however they are categorized.

Did the Buddha have any personal experience with maras and devas and supernatural beings in general?

Yes, throughout the suttas and many of the Mahayana sutras, like the Lotus Sutra, it is mentioned the various respledent powers that Gautama Buddha shows but also noteworthy is Buddha's personal attendant Ananda who is able to memorize everything the Buddha says but isn't able to get into the assembly of monks meeting after Buddha's death because he does not have samadhi.

Only when Ananda is able to attain samadhi (an actual achievement rather than just memorization) is he able to use super powers and join the assembly in discussion of Buddhism's fate.

And, if I'm not mistaken, the 31 planes of existence is something he taught. So, how did he come to know of them?

He viewed them directly when he entered samadhi, visiting each realm in turn. This is a scientific experiment because it is something that we ourselves can do, as well, after we achieve state of concentration (samadhi). Little is left to blind belief in Buddhism. The state of samadhi is also useful in investigating the other dharmas in Buddhism, such as the various mind objects and maras.