I have often thought about this and concluded it wasn't worth the effort. Ultimately it depends on what you want to do with it. If you want Galileo it be as similar as possible to the BeagleBone Black or Raspberry PI, it makes more sense to just buy one of those boards.If there is something about the Galileo you really need, you might be able to use the PI as a dumb terminal to the Galileo by using a VNC framebuffer server and networking as the connection. It is a bit crazy to throw that kind of hardware to the solution but it would be cheaper than any alternative. Performance could be a limiting factor though.
If you just want to write programs that output to a monitor you might be able to get something working with a simple VGA or HDMI connection. There is a lot of information about how to connect to VGA using a few resistors to generate the analog signal. It is pretty limited but might be possible to do some things with it. Due to slow Galileo IO it might need the addition of a CPLD or FPGA (for sure it is needed to do HDMI). The Gameduino has a FPGA which talks over SPI so this might be a good option. It lets you draw graphics but you likely won't be able to do Xorg user interfaces.
As Alex_T suggests, a PCIe card might be the best bet. It just will be pricey. It seems wrong to me spend more on the video card than a BeagleBone, PI or even Galileo itself. The Galileo is good, but it isn't good for everything. Pick the right tool for the job. But if your purpose is to have fun hacking, it will be interesting if you come up with a clever way of using the wrong tool for the job.