how do we know our framerates are stable?

Solution
The TIME for each frame should be stable (i.e. 1/60th second at 60FPS).

There are tools you can investigate at PCPER, however I believe to get accurate results you need their frame time software and other hardware (high speed capture card).

*There's an easier way and that's to simply see how SMOOTH the experience feels. For example, if running Half Life #1 or many older games the experience might feel BUTTER SMOOTH but a modern game also running 60FPS might have stutter and jutter (comparing what should be a "locked" 60FPS VSYNC'd experience).

PCPER worked with NVIDIA to attempt to define the user experience in terms of numbers so again if you want more info investigate there though I looked quite a while ago and didn't see any...
You can monitor them(3rd party software like Afterburner can do this) to see how much they play.

With high end card ware and frame rates over your monitor refresh, vsync can hold the frame rates at the max your monitor can handle.

If your frame rates fall often, turning down in game settings may help.

Not all users are sensitive to frame rate fluctuations. If you are not, do not worry about it.
 
The TIME for each frame should be stable (i.e. 1/60th second at 60FPS).

There are tools you can investigate at PCPER, however I believe to get accurate results you need their frame time software and other hardware (high speed capture card).

*There's an easier way and that's to simply see how SMOOTH the experience feels. For example, if running Half Life #1 or many older games the experience might feel BUTTER SMOOTH but a modern game also running 60FPS might have stutter and jutter (comparing what should be a "locked" 60FPS VSYNC'd experience).

PCPER worked with NVIDIA to attempt to define the user experience in terms of numbers so again if you want more info investigate there though I looked quite a while ago and didn't see any easily usable software.

(Do note that some programs like FRAPS may not have usable data for this type of test.)

Update:
I believe one of the issues with programs like FRAPS is that they'll record a frame even if it's only a PARTIAL FRAME so you could for example get as little as 15 full frames in a second and 45 partial frames despite the result saying it is "60FPS".
 
Solution
http://www.pcper.com/reviews/Graphics-Cards/Frame-Rating-New-Graphics-Performance-Metric

*Note that PCPER combines a high-end capture card which works in combination with their software, so again I'm not sure how the average person would do this unless there is software for the average person now I'm not aware of.

Might as well included GSYNC:
http://www.pcper.com/reviews/Graphics-Cards/Dissecting-G-Sync-and-FreeSync-How-Technologies-Differ

(GSYNC and FREESYNC use monitors which aren't locked to a preset time interval between refreshes, thus they produce a much smoother experience especially when the frame times are not even.)