What is the name of the view in games like Diablo 3, Starcraft, and Warcraft?

These games are example of parallel projections, so named because lines that are parallel in the 3D space remain parallel in the 2D display. In games these are usually - but not always - axonometric projections.

An isometric projection is a type of axonometric projection. Sometimes this term is used in games as a catch-all for all kinds of axonometric projections, but this is not accurate. In an isometric projection, not only do parallel lines remain parallel, but the angles between axes are preserved (hence iso, equal).

Warcraft: Orcs & Humans, and many other games which are often said to use "isometric graphics", actually are closer to dimetric projections (since they're hand-drawn, it's hard to tell and a bit inconsistent between sprites). Diablo (including III I believe) is using a real isometric projection.

Contrasting the parallel projection is the perspective projection, in which parallel lines get closer together and objects get smaller as they get further away.

This is generally referred to as isometric view.

While it is true that these games in the past used dimetric projection (nod to @JoeWreschnig), and that gamers and game devs call this "view from the corner" isometric projection (nod to @Beofett)... Both Diablo 3 and Starcraft 2 use something else - perspective projection.

Fun link: http://us.battle.net/d3/en/forum/topic/5149183613