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 younger brother before the release of Super Mario All-Stars,  after his recoloring in that game making him indistinguishable from Bowser, 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 World 8-4 and, according to the Encyclopedia Super Mario Bros., 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. Because of this, standing near the end of a castle in a way so that Bowser is barely seen on the right-hand side of the screen causes him to appear blue, but he will revert back to his correct colors if Mario or Luigi advances any further. In the Super Mario All-Stars version of the game, on the other hand, Blue Bowser is recolored to look identical to Bowser and also appears in D-4 in place of the fake version of him. Nonetheless, more recent sources rather stress Blue Bowser's body being blue as the main feature of the character, without mentioning him possibly having other coloring.

Super Mario Bros. Deluxe
Blue Bowser returns in Super Mario Bros. Deluxe. Here, he appears in World 8-4 of the game's Super Mario Bros.: The Lost Levels (referred to in this game as "Super Mario Bros. For Super Players") port, having the same role and appearance as that game.

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
Initially mentioned as just another Bowser in the Japanese guides of Super Mario Bros.: The Lost Levels, without specifying what was his relationship to Bowser beside not being his twin, in the character books of the '90s released before the release of Super Mario All-Stars Blue Bowser was described as being Bowser's younger brother,   with the Super Mario Zen Hyakka (Super Mario Complete Encyclopedia), a book written in collaboration with Nintendo, putting him as part of the King Tribe (「王族」) and thus a leader of the Koopa Troop and member of Bowser's royal family, along with the Koopalings and Bowser himself. He was also stated to be Bowser's brother in the Super Mario All-Stars Player's Guide, which marked the only time that concept was referenced in the English language. However, after the release of Super Mario All-Stars and his recoloring to look identical to Bowser, he started being considered akin to a Fake Bowser. This depiction is confirmed as well in Super Smash Bros. for Wii U. and even in the Super Mario Pia, a memorial book written in collaboration with Nintendo and released in 2015. Importantly, due to his recoloring in Super Mario All-Stars and his new status as Fake Bowser, no Japanese Nintendo Official Guidebook ever considered him a distinct character from the latters 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!"