I don't think there is a minimum requirement at all, other than screen size (with 800x600 or even smaller, it will look piss poor, and the settings dialogs probably won't fit on screen).
My copy of Code::Blocks has a virtual size of around 85-90 MiB and a working set of around 26-28 MiB (of which roughly 1/2 is mappings of system shared libraries, only 14 MiB are private).
Add a couple of megabytes depending on how big a project you want to load, and on how many editors you open at the same time. Obviously, keeping half a gigabyte worth of source files open in the editors will take (more than) half a gigabyte of memory, no surprise there.
A Windows system that can't make 15-20 MiB of physical memory available after boot is unusable. Launching Internet Exploder with an empty start page takes more than that, as do system tools like mmc.exe when you do anything but look at them. Windows Exploder dynamically allocates 40-60 MiB just for showing thumbnails when opening a folder with some images inside.