Wiktionary claims it is "magics", from how I read its page, but e.g. Ask.com claims it has no plural form. Considering that Wiktionary also claims that it is "usually uncountable", are there only certain situations it has a plural form in?
If you're referring to the idea in general, it's not countable. There's nothing to count. "Someone who practices magic", "friendship is magic", or "magic powers this device" would all fit this pattern.
However, if you're referring to some specific kind, it's countable. So "the magics of necromancy and enchantment" is legitimate: it's referring to two different but related things. (Similarly, "the peoples of England and Scotland" refers to each separate group of people, and "the monies allocated were spent primarily in two ways" does the same thing for "money".) This is not a very common usage, though, since for most purposes there's really no reason to make a distinction between different kinds of something that's imaginary anyway.
Or here's another example:
Ain's machine was built under the Black Spike surrounded by deep water, a work of genius tainted by madness. They had called it the Sixth Magic. No matter its power; it was flawed and unclean from the beginning. Mael's last accomplishment was supposed to elevate the magics above the stain of Ain's madness.
Alan and Nathan have both answered this, I'm only adding some references
Magic is, indeed, an uncountable noun.
However, an instance of magic is singular and so has often been made plural with the addition of an S.
Kipling writing in Strand Magazine in 1906
What's that for—magic?’ said Una... ‘One of my little magics,’ he answered. - sourced from the OED
Another example from the OED
...you keep bumping into these small magics — things people would like to believe, just as we'd all rather like to believe in haunted houses and water witching
As for the other conversation about magick or magik- it pre-dates the now standard spelling
Chaucer, back around the turn of the 14th century
Clerkes eke, which konne wel Al this magik naturel..thrugh which magik To make a man ben hool or syk.
Shakespeare himself was a bit of a fan of Magick (all from 1st folio spellings c1623)
Magick Verses haue contriu'd his end. - Henry VI part 1
There's Magick in thy Maiestie - Winter's tale
And plucke my Magick garment from me - The Tempest
And, an example in the plural...
Bring your Magicks, Spels, and Charmes, To enflesh my thighs, and armes. From Robert Herrick's Hesperedes
The plural form of magic is magics.
Magic is usually used as a mass or non-count or uncountable (pick a term) noun, so it will usually be used in the singular.
Sometimes words we think are only used as a mass noun, such as money and imagination can be used as count nouns, so it cannot be said that you'll never see magics.
Magical arts is a close equivalent.
In most common usage "magic" is an uncountable noun. Using the word "magics" generally implies a context of a specific religious/fictional belief-structure that has internally-defined concepts of different kinds of magic
For example: As an outsider witnessing a group preforming four magic-rituals I would probably refer to the four rituals collectively as "magic". A member of the group might refer to the first three rituals as "spirit magic", but they may refer the four rituals as "magics" if they believed the fourth ritual to be a distinct class of "earth magic". The next day I might say "They showed by their magics", but using the word "magics" implies that they told me they were "magics", and that I am speaking from the internal viewpoint of their belief system, although it does not imply that I share their belief. I am merely speaking in a specific context of their beliefs.