5GB at present, bob, though they're planning to expand it a bit
"We've designed Windows Live Hotmail storage to grow with you, but at a reasonable pace. That means you should have plenty of storage unless you suddenly want to store the planet Jupiter on Hotmail, in which case we'll send you a nice e-mail asking you to please not try to store planets on Windows Live Hotmail (although gradual storage of moons and asteroids is ok)."
Presumably this is in response to googlemail, whose storage space is also not unlimited but increases all the time (counter says mine's up to 7.2GB)