(of a manifestation or event) attributed to some force beyond scientific understanding or the laws of nature.
By applying this dictionary definition we can see that most of science is supernatural. For example, gravity. It is still a mystery "beyond scientific understanding" hence supernatural by definition (see above).
Kurt Godel's "Incompleteness Theorem" proves that for everything science can explain there are many more new things to understand. This means that science will always be incomplete. This theorem has the online support of Stephen Hawking as a free essay.
As science can never fully prove anything it remains by definition (see above) supernatural.
Now if you mean "ghosts" or "esp" etc each in its turn has a basis in incomplete science. For example there are numerous new theorems that prove other ghostly dimensions exist in the same space simultaneously. On the quantum level inexplicable ghostly and other events occur such as bilocation. Bilocation was once solely the province of quacks and weirdos at seances. On a quantum level the laws of nature go haywire.
Therefore by simply referring to the actual meaning of supernatural we can easily see we are surrounded by and exist due to supernatural phenomena.