Bug introduced in 8 or earlier and persisting through 13.1.0
Reported to the support as [CASE:3968587]. Published on Wolfram Community.
In the presence of alpha channel ImageCrop doesn't remove borders at all despite the fact that the latter are exactly uniform (both in the color channels and in the alpha channel). Here is an example of inconsistent behavior of ImageCrop (checked with versions 8.0.4, 9.0.1, 11.2.0 and 11.3.0):
img = Rasterize[
Graphics[{Circle[{0, 0}, 1],
Text[Style[l, FontFamily -> "Times"], {1.2, 0}]}, Frame -> False,
PlotRange -> {{.9, 1.3}, All}], "Image", Background -> None];
Show[#, Frame -> True, FrameTicks -> False,
PlotRangePadding -> None] & /@
{img, ImageCrop[img], ImagePad[img, -BorderDimensions[img, 0]]}
The built-in ImageCrop function "effectively removes borders from image whose pixel value distribution is almost uniform" (emphasis mine). I need an efficient cropping function which removes borders whose pixel values are identical. What is the best way to do this in Mathematica? I don't need support for 3D images, but images with an alpha channel should be supported.

ImageCropis "smarter" than I need! – Alexey Popkov Mar 02 '13 at 11:55SetOptions[ImageCrop, Tolerance -> 0.03]and get the "new" behavior. – Mr.Wizard Mar 02 '13 at 12:26ImageCropis a crap. – Alexey Popkov Mar 02 '13 at 20:53