Bowser's Brother

Blue Bowser (direct translation from the Japanese 「クッパ・アオ」) is a member of Bowser's species who looks very similar to Bowser, except for the brown and blue color of his skin and shell. He appears exclusively in the Family Computer Disk System version of Super Mario Bros.: The Lost Levels. While considered to be Bowser's brother before the release of Super Mario All-Stars, after his replacement with other characters indistinguishable from Bowser in said game the depiction of his identity changed over time, being first considered like a Fake Bowser,  then a blue-bodied Bowser whose identity is unknown.

Super Mario Bros.: The Lost Levels
The only game so far that actually features Blue Bowser is the Family Computer Disk System version of Super Mario Bros.: The Lost Levels. There, he appears in both World 8-4 and World 9-3. He tries to stop Mario or Luigi both by throwing hammers at them and by breathing fire. While distinguished from Bowser through the color of his skin and shell, when defeated with fireballs he does not turn into one of Bowser's minions, revealing his actual identity as a member of Bowser's species, distinct from that of the Fake Bowsers. On World D-4, a fake version of him appears that only breathes fire and, when defeated with fireballs, is revealed to be a Spiny.

The color of his skin and shell are actually obtained through a palette swap commonly used in castle sections of the game, except for the parts in which the boss is fought. In the Super Mario All-Stars version of the game, on the other hand, Blue Bowser is not featured and only characters who look identical to Bowser appear in World 8-4, 9-3, and also D-4.

Super Smash Bros. for Wii U
While Super Smash Bros. for Wii U does not actually feature Blue Bowser, the eighth recolor of Bowser is said to be inspired by him.

Family relationship
Before the release of Super Mario All-Stars, books related to Super Mario Bros.: The Lost Levels described Blue Bowser as being Bowser's brother, with the Super Mario Complete Encyclopedia specifically indicating him as Bowser's younger brother and a member of his Royal Family, along with the Koopalings and Bowser himself. After the release of Super Mario All-Stars and his replacement with characters who look identical to Bowser, he started being considered akin to a Fake Bowser and no longer a member of Bowser's Royal Family. This depiction is confirmed as well in Super Smash Bros. for Wii U. Importantly, due to his absence from Super Mario All-Stars, no Japanese Nintendo Official Guidebook ever mentioned him until the release of the Encyclopedia Super Mario Bros.. There, he is clearly distinguished from Fake Bowsers, but his identity is stated to be unknown, leaving his current relationship with Bowser unexplained.

Super Smash Bros. for Wii U tip

 * "A Bowser Impostor?! In Super Mario Bros.: The Lost Levels, Mario fights a blue fake Bowser before the real thing. That blue fake is his eighth color in this game!"