What are your computing needs? You can probably build a tiny system that mounts to the VESA mount on the back of your monitor and use a wireless KB/mouse. The only cables would be the power cords going down the back of your desk and a network cable (if not WiFi). Here's one such configuration:
Your choice Sandy Bridge CPU (I'd recommend Core i3 2100T)
Your choice mini ITX 1155 motherboard
Your choice RAM that fits motherboard
Your choice SSD
Mini Box M350 case with Pico PSU and VESA mount
Your choice wireless KB/mouse