Motherboard USB cable splitters don't exist because of the way the USB standard works. However, if your motherboard has limited USB connections and you need more, there are a lot of other ways to get more USB connections.
If you still have unused USB headers on your motherboard to plug into, you can get a USB bracket. USB brackets function like USB splitters. You just need an available expansion card slot that you can mount the bracket on.
This is the simplest option - a USB bracket won't draw any additional power and will use your motherboard's built in USB controller, it just 'splits' the connection from the motherboard and gives you multiple external USB ports to plug devices into. If you have an unused USB controller on your motherboard and an available expansion card slot, this is probably the best option for you.
PCI to USB Cards
If you've used all of your motherboard's USB controllers, never fear, there are more options for you. You can get a PCI to USB card, a PCI expansion card that plugs into a standard PCI socket. It will add additional USB ports to your computer, using USB controlling hardware built into the PCI card so that your motherboard can handle many more USB devices even if it's maxed out.
Owners of newer motherboards may have few PCI card slots and more PCI-E card slots. In this case, you can get a PCI-E to USB expansion card instead. While these PCI and PCI-E cards don't function as USB splitters, they will add many more USB ports to existing hardware.
Image Source: Wikimedia Commons/Ricardo Moctezuma
USB 3.0 Expansion Cards
If your motherboard has an available PCI-E slot, you can also use a USB 3.0 - PCI-E expansion card. This will allow you to get much faster speeds for devices which support and can use it, such as external drives. Since most motherboards in use don't come with USB 3.0 hardware, this is a great way to upgrade your system to be USB 3.0 capable if you don't feel like buying a new motherboard yet.
You can also buy a USB hub. This is a device that will plug into a USB port and give you more ports to plug your USB devices into. These devices usually sit on your desk, so they are also a good option if your USB ports are located in hard to reach places, to make them easier to access. A big advantage with these is that they're portable; you can plug it into your laptop and then quickly unplug it and plug it into another PC. With USB brackets and PCI to USB cards, you have to open your computer case to remove the part.
Some USB keyboards and other peripherals also come with built-in USB hubs, which can help to reduce the cable mess.
Image Credit: Wikimedia Commons/Ds13