Stanley Kubrick shot all of his films after Killer's Kiss for widescreen. He only asked for them to be shown unmatted when possible on the old laserdisc masters he approved back in 1991-1992. He died before having a chance to approve new transfers made for the 16x9 format. The decision to go open matte had more to do with wanting to use available image instead of letterbox bars since it wasted a lot of resolution. He protected his films for either ratio, so it was a smart move. Now that we have anamorphic widescreen, it's a moot point.

Here's how his films should be shown:

Killer's Kiss - 1.33:1
The Killing - 1.75:1
Paths of Glory - 1.75:1
Spartacus - 2.20:1 (70mm prints, preferable) or 2.35:1 (35mm scope prints, which is fine too)
Lolita - 1.66:1
Dr. Strangelove - 1.66:1
2001: A Space Odyssey - 2.20:1 (obviously)
A Clockwork Orange - 1.66:1
Barry Lyndon - 1.66:1
The Shining - 1.85:1
Full Metal Jacket - 1.85:1
Eyes Wide Shut - 1.85:1

Also, the new DVDs for The Shining and Eyes Wide Shut will be 1.85:1 anamorphic widescreen. Eyes Wide Shut will be uncut. A Clockwork Orange will be 1.66:1 anamorphic widescreen.