Equivalent of the old beauty button for subdivide? I'd like to subdivide a mesh, but only cut the long edges of the quads. So, with all faces selected, I want to halve the quads instead of quartering them 

Beauty and short were settings for the subdivide tool. They did that wonderfully. Seems the functionality has been replaced or removed.
Look under options and you know what I mean.

To illustrate it further:



The top mesh is the base, the middle mesh is the result of an ordinary subdivide and the lower mesh has only it's long edges cut. Imagine thousands of long faces that need more topology. 

Why don't I want to do it manually? Becaus or cases like this one:



What's today's way of doing that?
You can select an Edge Ring (sort of the opposite of an Edge Loop) with Ctrl+Alt+Right Click and subdivide that.



Also remember there's Subdivide Smooth as well, which is nice for interpolating the curvature of the model (though it cannot do this on a flat 2D surface like this example).

Unfortunately it won't really help in that Icosphere case though.