With two reservations - I'm not using KVM, and I'm not an admin, just a laptop owner - I've had almost no problems with the Debian unstable "sid" release, using it every day (and night) doing all kinds of stuff for years.
On the contrary: I experienced a lot of small problems (e.g., Evince not showing some special characters) suddenly remedied by the new software, with no following decrease in stability at all.
Here, the Debian people describe sid like this:
"The 'unstable' distribution is where active development of Debian occurs. Generally, this distribution is run by developers and those who like to live on the edge."
With no disrespect whatsoever - I love their system - I think this is a massive exaggeration. The reason they express themselves that way, is that the Debian people are really into stability. What they call the stable release, we mere mortals would probably refer to as stainless, rock-solid stability.
But, as a last note of caution, as said in another answer, it all depends what you're doing. If you run a server, and your trademark punch is never-failing availability, of course you should use the stable release. That's an extreme example, and I made it that way on purpose, because it is my notion that in general, you should not be afraid of the newer versions.