How to have an I-Beam bend as little as possible I have an I-Beam cantilever beam and apply a force to the free end. If I want the displacement in the vertical axis of the end being forced to be as small as possible from that when no force is present will I want the web or flange to be bigger?
I have since done a few beam tests and these are my results: 

These would make it appear that in fact a larger flange means that there is more displacement don't they? 
 A: It depends on the stress you need to support because of buckling as is visible in your first diagram. This also means it depends on how the force is applied - at a point, at the top, across the end?
For small forces (no worries about buckling) you want the tallest thinnest beam since you are maximizing the second moment of area for constant area. However in the limit that will always buckle so now you have to make it thicker (in the middle) and shorter - with any spare material relegated to the edges.
I don't think there is a single right answer; it really does depend on the max stress you must be able to sustain.
A: You want the 2 flanges at either side to be bigger.  The reason the I-Beam cross-section is shaped that way is because it is the material furthest from the centroid (i.e. the 2 flanges) that is providing the most stiffness against bending. The material closer to the centroid is not providing as much stiffness, so it makes sense to take most of that away to reduce the weight (and improve the stiffness:weight ratio).
Bending stiffness is related to the second moment of area of the cross-section, which for an I-Beam is larger in the direction of bending that is aligned with the central web. If you look at any structural application where I-Beams are used, they are always oriented that way.
