The 32bit version of Windows 7 required 16GB of hard drive space for a vanilla installation, so without any additional applications, and without Microsoft Office installed. Thanks to things like the page file, hibernate file, system restore points, and keeping updates locally on disk, Windows 7 consumed more space over time. Since Windows RT will be 32bit, it makes the most sense to keep the figures for 32bit Windows 7 in mind.
On Reddit, Microsoft's Surface test manager, Ricardo Lopez, detailed how much space Windows RT will take up: 12GB. However, and this is crucial, this includes Office RT 2013, and "a bunch of apps". In other words, it is considerably smaller than its closest predecessor.
However, this compares rather unfavourably to its competition. Anyone who has ever downloaded an Android ROM knows they're about 130-150MB in size (at least, for CyanogenMod); the Android Compatibility Definition Document for Jelly Bean demands at least 340MB for kernel and userspace. I found it hard to find exact information on iOS - but it's reported that it's less than 1GB in size.
There's some good reasons why it's larger, though. First of all, Microsoft's Office team was unable to create a Metro Office in time, and as such, even the RT version includes the entire old desktop stack - just to run Office (you can't install anything else on the desktop). This most likely takes up a considerable amount of space. Whether or not this desktop stack is a good thing to have on a tablet is up to you (hint: it's not).
On top of that - although I'm not sure - my guess is that Windows RT includes a heck of a lot more drivers than iOS and Android do. Supposedly, it's as compatible with hardware as plain Windows, and I think that requires a lot more space for drivers than iOS and Android offer. Again - whether or not that's a good thing is up to you (hint: it is).
I am left wondering how Windows RT handles the buildup of cruft. Even Windows 7 grew in size over time, with bits and pieces left behind all over the place. Those few additional GBs of wasted space might not be an issue on machines with terabyte hard drives, but on a 32GB Surface, that's going to add up. Will users be dumped to the desktop to use that horrid 'free up space'-wizard? On a tablet?
That'd be fun.