I created this inset on a cylindrical part of the model, then decided I didn't want the inset anymore. What's the easiest way to remove it? I tried Dissolving Faces and Dissolving Edges, to no avail.
Delete edge loops
Switch to face select mode (⎈ Ctrl↹ Tab>Faces)
Select the face loop inside the inset (⎇ Alt RMB on an edge. See How can edge rings be selected in a predictable way?)
Switch to edge select mode (⎈ Ctrl↹ Tab)
⎈ Ctrl⇧ Shift⎇ Alt RMB on an edge to deselect the edge ring.
⌦ Delete> Edge loops (the menu accelerator G can be used for extra speed)
Scale and remove doubles
This is only really practical if your inset is aligned to an axis. Setting up custom axes and such would sorta defeat the purpose. However, if your inset is aligned (as it appears in your case), then this might well be faster than the first method.
Select the inset as shown in your screenshot
Scale to 0 along the Z (or whatever axis your inset is aligned to) (SZ
W> Remove Doubles, or WE if you use the menu accelerator.
⌦ Delete> Faces (⌦ DeleteF with the menu accelerator).
Apologies in advance if the gifs are too fast. I was attempting to show what it looks like at sortof-full speed, but I'm not sure if it's possible to follow at gif framerates..