Sort of. I'm not sure if most of you know this, but Nintendo is responsible for the formation of the Playstation. In 1988, Nintendo wanted to create a compact disk based system and signed a contract with Sony, who would be in charge with the creation of the new "SNES - CD" format. Sony was also going to develop a system that would be able to use SNES cartridges and SNES-CDs. But when Nintendo went over the contract in 1991, they realized that Sony would have too much power over the CDs and scrapped the project. After that, Sony decided to create their own system using the new technology they had developed.
So then Nintendo went to Phillips for help and we all know what happened then...
Hotel Mario, Link: The Faces of Evil, Zelda's Adventure
For more information read the history of the Playstation at Wikipedia and go to the N-Sider for the full article.
Also, let me throw in this one speculation that I have that is probably false. Sega might have been responsible for the Xbox. The Sega Dreamcast was powered by Windows CE, an OS meant for use in consoles and portable devices. The Dreamcast was discontinued in 2001 (US) and the Xbox was released in November 2001 (US). Now, the reason I think this is for the striking similarities between the two consoles. For example, both consoles ran Microsoft's Direct X (Dreamcast ran DirectX 7 and Xbox ran DirectX 8.1). The Xbox controller looks very similar to the Dreamcast. You could say that Microsoft kept the layout of the Dreamcast controller and added about 7 new buttons and and an extra control stick.
The Xbox controller also had the ability to attach a memory card to it, much like the Dreamcast's VMU memory system. Both systems also came with a built-in network adapter.
So take these in consideration the next time you pick up your controller.