Is there a way to get OSX style file previews in the file browser?

In the default file browser of Mac OS X, pressing space will preview the file in question.

Is there already something similar that I haven't found, or is there a way to add the functionality to Ubuntu?

There is a program that I think do the thing you asked for (not 100% sure since I never used OSX), it's called sushi. It basically open a windows giving you preview of all files and directories pressing the spacebar.
It is in the default repository so to install use can type in a terminal

sudo apt-get install gnome-sushi

and you have to restart nautilus: type in the terminal

nautilus -q

to close it and click on the home folder icon on the dash to start it again.

There is also Gloobus Preview. It works very well and I've been using it for years.