I've had my dream monitor for about half a year now: the Sony GDM-FW900.
...Well, I suppose it wouldn't hurt to throw in a Wacom Cintiq 24HD (touch-enabled) on the "dream monitor" list. Prop that below my FW900 and I could use it as a virtual cockpit interface when I'm not attempting to draw on it.
As for monitors that only exist in dreams...well, how about a flat-panel with no native resolution (meaning that non-native resolutions don't look like utter crap, but it's still capable of 4K and beyond), no input lag, perfect viewing angles, a color gamut as wide as the eye can perceive, hardware LUT support, and of course, a Wacom dual-digitizer configuration for pen and touch input?