Super Kaio-ken is a combination of the Super Saiyan transformation and the Kaio-ken technique, which can only be utilized when the user is dead due to its 100% chance of incurring death on a living user.
Goku uses this technique while fighting in the Other World Tournament against Pikkon. By using the power of Kaio-ken while in his Super Saiyan form, Goku gains a massive power increase, which is statistically equivalent to that of a Super Saiyan 2, by taking the 2x multiplier of these forms into consideration. Goku is seen punching Pikkon towards an asteroid orbiting the Other World Stadium, after which he reverts to his Super Saiyan form.
Goku is never seen using this technique again after he used it against Pikkon, as he didn't have the required ki control to use it effectively even while deceased.
Without this perk a living Super Saiyan wouldn't be able to handle the stress caused by the enormous ki build up and thus die.
Appearances in games
In the Dragon Ball Z arcade game by Banpresto, Goku has the Kaio-ken as one of his special moves, and he's able to use it even in his Super Saiyan form. Similarly, in Super Dragon Ball Z, Goku is able to use Super Kaio-ken by transforming into a Super Saiyan, and then using Kaio-ken.
In the Dragon Ball Z Collectible Card Game, Goku can use this Kaio-ken in combination with any of his appearing Super Saiyan forms: Super Saiyan, 2nd Grade Super Saiyan, Super Saiyan 2, Super Saiyan 3, Golden Great Ape, and Super Saiyan 4.
In Jump Super Stars, Goku can oddly use this in his Battle Koma 5 as his Special B/Up Special, being able to use it as a charged attack which increases the amount of physical blows he will perform in the brief combo for that one attack. It is used in the same fashion as the Super Kaio-ken (due to BK5 Goku being in Super Saiyan mode by default), only Goku simply has the red aura's outline with no actual change to his colors inside of said aura. It has been somewhat rectified in Jump Ultimate Stars, with Goku having his Battle Koma 5 being in his normal form instead.